Uniform 8-polytope

{{short description|Polytope contained by 7-polytope facets}} {| class="wikitable skin-invert-image" style="float:right; margin-left:1em; width:300px" |+ Graphs of three [[List of regular polytopes#Dimension 5 and higher|regular]] and related [[uniform polytope]]s. |- valign=top align=center |colspan=4|[[File:8-simplex t0.svg|100px]]<br/>[[8-simplex]] |colspan=4|[[File:8-simplex t1.svg|100px]]<br/>[[Rectified 8-simplex]] |colspan=4|[[File:8-simplex t01.svg|100px]]<br/>[[Truncated 8-simplex]] |- valign=top align=center |colspan=4|[[File:8-simplex t02.svg|100px]]<br/>[[Cantellated 8-simplex]] |colspan=4|[[File:8-simplex t03.svg|100px]]<br/>[[Runcinated 8-simplex]] |colspan=4|[[File:8-simplex t04.svg|100px]]<br/>[[Stericated 8-simplex]] |- valign=top align=center |colspan=4|[[File:8-simplex t05.svg|100px]]<br/>[[Pentellated 8-simplex]] |colspan=4|[[File:8-simplex t06.svg|100px]]<br/>[[Hexicated 8-simplex]] |colspan=4|[[File:8-simplex t07.svg|100px]]<br/>[[Heptellated 8-simplex]] |- valign=top align=center |colspan=4|[[File:8-cube t7.svg|100px]]<br/>[[8-orthoplex]] |colspan=4|[[File:8-cube t6.svg|100px]]<br/>[[Rectified 8-orthoplex]] |colspan=4|[[File:8-cube t67.svg|100px]]<br/>[[Truncated 8-orthoplex]] |- valign=top align=center |colspan=6|[[File:8-cube t57.svg|150px]]<br/>[[#The B8 family|Cantellated 8-orthoplex]] |colspan=6|[[File:8-cube t47.svg|150px]]<br/>[[Runcinated 8-orthoplex]] <!--|colspan=4|[[File:8-cube t37.svg|100px]]<br/>[[Stericated 8-orthoplex]]--> |- valign=top align=center <!--|colspan=4|[[File:8-cube t27.svg|100px]]<br/>[[Pentellated 8-orthoplex]]--> |colspan=6|[[File:8-cube t17.svg|150px]]<br/>[[Hexicated 8-orthoplex]] |colspan=6|[[File:8-cube t02.svg|150px]]<br/>[[Cantellated 8-cube]] |- valign=top align=center |colspan=4|[[File:8-cube t03.svg|100px]]<br/>[[Runcinated 8-cube]] |colspan=4|[[File:8-cube t04.svg|100px]]<br/>[[Stericated 8-cube]] |colspan=4|[[File:8-cube t05.svg|100px]]<br/>[[Pentellated 8-cube]] |- valign=top align=center |colspan=6|[[File:8-cube t06.svg|150px]]<br/>[[Hexicated 8-cube]] |colspan=6|[[File:8-cube t07.svg|150px]]<br/>[[Heptellated 8-cube]] |- valign=top align=center |colspan=4|[[File:8-cube t0.svg|100px]]<br/>[[8-cube]] |colspan=4|[[File:8-cube t1.svg|100px]]<br/>[[Rectified 8-cube]] |colspan=4|[[File:8-cube t01.svg|100px]]<br/>[[Truncated 8-cube]] |- valign=top align=center |colspan=4|[[File:8-demicube t0 D7.svg|100px]]<br/>[[8-demicube]] |colspan=4|[[File:8-demicube t01 D7.svg|100px]]<br/>[[Truncated 8-demicube]] |colspan=4|[[File:8-demicube t02 D7.svg|100px]]<br/>[[Cantellated 8-demicube]] |- valign=top align=center |colspan=6|[[File:8-demicube t03 D7.svg|150px]]<br/>[[Runcinated 8-demicube]] |colspan=6|[[File:8-demicube t04 D7.svg|150px]]<br/>[[Stericated 8-demicube]] |- valign=top align=center |colspan=6|[[File:8-demicube t05 D7.svg|150px]]<br/>[[Pentellated 8-demicube]] |colspan=6|[[File:8-demicube t06 D7.svg|150px]]<br/>[[Hexicated 8-demicube]] |- valign=top align=center |colspan=4|[[File:Gosset 4 21 polytope petrie.svg|100px]]<br/>[[4 21 polytope|4₂₁]] |colspan=4|[[File:Gosset 1 42 polytope petrie.svg|100px]]<br/>[[1 42 polytope|1₄₂]] |colspan=4|[[File:2 41 polytope petrie.svg|100px]]<br/>[[2 41 polytope|2₄₁]] |} In [[Eight-dimensional space|eight-dimensional]] [[geometry]], an '''eight-dimensional polytope''' or '''8-polytope''' is a [[polytope]] contained by 7-polytope facets, each [[6-polytope]] [[Ridge (geometry)|ridge]] being shared by exactly two [[7-polytope]] [[Facet (mathematics)|facets]].

A '''uniform 8-polytope''' is one which is [[vertex-transitive]], and constructed from [[uniform 7-polytope]] facets.

== Regular 8-polytopes == Regular 8-polytopes can be represented by the [[Schläfli symbol]] {p,q,r,s,t,u,v}, with '''v''' {p,q,r,s,t,u} 7-polytope [[Facet (mathematics)|facets]] around each [[Peak (geometry)|peak]].

There are exactly three such [[List of regular polytopes#Convex|convex regular 8-polytopes]]: # {3,3,3,3,3,3,3} - [[8-simplex]] # {4,3,3,3,3,3,3} - [[8-cube]] # {3,3,3,3,3,3,4} - [[8-orthoplex]]

There are no nonconvex regular 8-polytopes.

== Characteristics == The topology of any given 8-polytope is defined by its [[Betti number]]s and [[torsion coefficient (topology)|torsion coefficient]]s.<ref name="richeson">Richeson, D.; ''Euler's Gem: The Polyhedron Formula and the Birth of Topology'', Princeton, 2008.</ref>

The value of the [[Euler characteristic]] used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 8-polytopes, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.<ref name="richeson"/>

Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.<ref name="richeson"/>

== Uniform 8-polytopes by fundamental Coxeter groups == Uniform 8-polytopes with reflective symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the [[Coxeter-Dynkin diagram]]s:

{| class=wikitable |- !# !colspan=3|[[Coxeter group]] !Forms |- |1||A₈|| [3⁷]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}||135 |- |2||BC₈||[4,3⁶]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}||255 |- |3||D₈||[3^5,1,1]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node}}||191 (64 unique) |- |4||[[E8 (mathematics)|E₈]]||[3^4,2,1]||{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}||255 |} Selected regular and uniform 8-polytopes from each family include: # [[Simplex]] family: A₈ [3⁷] - {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}} #* 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular: #*# {3⁷} - [[8-simplex]] or ennea-9-tope or enneazetton - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}} # [[Hypercube]]/[[orthoplex]] family: B₈ [4,3⁶] - {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}} #* 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones: #*# {4,3⁶} - [[8-cube]] or ''octeract'' - {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}} #*# {3⁶,4} - [[8-orthoplex]] or ''octacross'' - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}} # [[Demihypercube]] D₈ family: [3^5,1,1] - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}} #* 191 uniform 8-polytopes as permutations of rings in the group diagram, including: #*# {3,3^5,1} - [[8-demicube]] or ''demiocteract'', '''1₅₁''' - {{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}; also as h{4,3⁶} - {{CDD|node_h|4|node|3|node|3|node|3|node|3|node|3|node|3|node}} #*# {3,3,3,3,3,3^1,1} - [[8-orthoplex]], '''5₁₁''' - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}} # [[Semiregular E-polytope|E-polytope family]] E₈ family: [3^4,1,1] - {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}} #* 255 uniform 8-polytopes as permutations of rings in the group diagram, including: #*# {3,3,3,3,3^2,1} - [[Thorold Gosset]]'s semiregular '''[[Gosset 4 21 polytope|4₂₁]]''', {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}} #*# {3,3^4,2} - the uniform '''[[Gosset 1 42 polytope|1₄₂]]''', {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}, #*# {3,3,3^4,1} - the uniform '''[[Gosset 2 41 polytope|2₄₁]]''', {{CDD|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}

=== Uniform prismatic forms === There are many [[Uniform polytope|uniform]] [[Prismatic polytope|prismatic]] families, including:

{| class="wikitable collapsible collapsed" !colspan=12|Uniform 8-polytope prism families |- !# !colspan=2|[[Coxeter group]] ![[Coxeter-Dynkin diagram]] |- !colspan=4|7+1 |- |1||A₇A₁|| [3,3,3,3,3,3]×[&nbsp;]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|2|node}} |- |2||B₇A₁||[4,3,3,3,3,3]×[&nbsp;]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|2|node}} |- |3||D₇A₁||[3^4,1,1]×[&nbsp;]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|2|node}} |- |4||[[E7 (mathematics)|E₇]]A₁||[3^3,2,1]×[&nbsp;]||{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|2|nodea}} |- !colspan=4|6+2 |- |1||A₆I₂(p) ||[3,3,3,3,3]×[p] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}} |- |2||B₆I₂(p) ||[4,3,3,3,3]×[p] ||{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|p|node}} |- |3||D₆I₂(p) ||[3^3,1,1]×[p] ||{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|p|node}} |- |4||E₆I₂(p) ||[3,3,3,3,3]×[p] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}} |- !colspan=4|6+1+1 |- |1||A₆A₁A₁ ||[3,3,3,3,3]×[&nbsp;]x[&nbsp;] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}} |- |2||B₆A₁A₁ ||[4,3,3,3,3]×[&nbsp;]x[&nbsp;] ||{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|2|node}} |- |3||D₆A₁A₁ ||[3^3,1,1]×[&nbsp;]x[&nbsp;] ||{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|2|node}} |- |4||E₆A₁A₁ ||[3,3,3,3,3]×[&nbsp;]x[&nbsp;] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}} |- !colspan=4|5+3 |- |1||A₅A₃|| [3⁴]×[3,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|3|node|3|node}} |- |2||B₅A₃||[4,3³]×[3,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|3|node|3|node}} |- |3||D₅A₃||[3^2,1,1]×[3,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|3|node|3|node}} |- |4||A₅B₃|| [3⁴]×[4,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|4|node|3|node}} |- |5||B₅B₃||[4,3³]×[4,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|4|node|3|node}} |- |6||D₅B₃||[3^2,1,1]×[4,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|4|node|3|node}} |- |7||A₅H₃|| [3⁴]×[5,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|5|node|3|node}} |- |8||B₅H₃||[4,3³]×[5,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|5|node|3|node}} |- |9||D₅H₃||[3^2,1,1]×[5,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|5|node|3|node}} |- !colspan=4|5+2+1 |- |1 ||A₅I₂(p)A₁|| [3,3,3]×[p]×[&nbsp;]|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|p|node|2|node}} |- |2 ||B₅I₂(p)A₁|| [4,3,3]×[p]×[&nbsp;]|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|p|node|2|node}} |- |3 ||D₅I₂(p)A₁|| [3^2,1,1]×[p]×[&nbsp;]|| {{CDD|nodes|split2|node|3|node|3|node|2|node|p|node|2|node}} |- !colspan=4|5+1+1+1 |- |1 ||A₅A₁A₁A₁|| [3,3,3]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|2|node|2|node}} |- |2 ||B₅A₁A₁A₁|| [4,3,3]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|2|node|2|node}} |- |3 ||D₅A₁A₁A₁|| [3^2,1,1]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|nodes|split2|node|3|node|3|node|2|node|2|node|2|node}} |- !colspan=4|4+4 |- |1||A₄A₄||[3,3,3]×[3,3,3]||{{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|3|node}} |- |2|| B₄A₄||[4,3,3]×[3,3,3]||{{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|3|node}} |- |3||D₄A₄||[3^1,1,1]×[3,3,3]||{{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|3|node}} |- |4|| F₄A₄||[3,4,3]×[3,3,3]||{{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|3|node}} |- |5|| H₄A₄||[5,3,3]×[3,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|3|node}} |- |6|| B₄B₄||[4,3,3]×[4,3,3]||{{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|3|node}} |- |7||D₄B₄||[3^1,1,1]×[4,3,3]||{{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|3|node}} |- |8|| F₄B₄||[3,4,3]×[4,3,3]||{{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|3|node}} |- |9|| H₄B₄||[5,3,3]×[4,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|3|node}} |- |10||D₄D₄||[3^1,1,1]×[3^1,1,1]||{{CDD|nodes|split2|node|3|node|2|nodes|split2|node|3|node}} |- |11|| F₄D₄||[3,4,3]×[3^1,1,1]||{{CDD|node|3|node|4|node|3|node|2|nodes|split2|node|3|node}} |- |12|| H₄D₄||[5,3,3]×[3^1,1,1]||{{CDD|node|5|node|3|node|3|node|2|nodes|split2|node|3|node}} |- |13|| F₄×F₄||[3,4,3]×[3,4,3]||{{CDD|node|3|node|4|node|3|node|2|node|3|node|4|node|3|node}} |- |14|| H₄×F₄||[5,3,3]×[3,4,3]||{{CDD|node|5|node|3|node|3|node|2|node|3|node|4|node|3|node}} |- |15|| H₄H₄||[5,3,3]×[5,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|3|node}} |- !colspan=4|4+3+1 |- |1 ||A₄A₃A₁|| [3,3,3]×[3,3]×[&nbsp;]|| {{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|2|node}} |- |2 ||A₄B₃A₁|| [3,3,3]×[4,3]×[&nbsp;]|| {{CDD|node|3|node|3|node|3|node|2|node|4|node|3|node|2|node}} |- |3 ||A₄H₃A₁|| [3,3,3]×[5,3]×[&nbsp;]|| {{CDD|node|3|node|3|node|3|node|2|node|5|node|3|node|2|node}} |- |4 ||B₄A₃A₁|| [4,3,3]×[3,3]×[&nbsp;]|| {{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|2|node}} |- |5 ||B₄B₃A₁|| [4,3,3]×[4,3]×[&nbsp;]|| {{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|2|node}} |- |6 ||B₄H₃A₁|| [4,3,3]×[5,3]×[&nbsp;]|| {{CDD|node|4|node|3|node|3|node|2|node|5|node|3|node|2|node}} |- |7 ||H₄A₃A₁|| [5,3,3]×[3,3]×[&nbsp;]|| {{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|2|node}} |- |8 ||H₄B₃A₁|| [5,3,3]×[4,3]×[&nbsp;]|| {{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|2|node}} |- |9 ||H₄H₃A₁|| [5,3,3]×[5,3]×[&nbsp;]|| {{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|2|node}} |- |10 ||F₄A₃A₁|| [3,4,3]×[3,3]×[&nbsp;]|| {{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|2|node}} |- |11 ||F₄B₃A₁|| [3,4,3]×[4,3]×[&nbsp;]|| {{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|2|node}} |- |12 ||F₄H₃A₁|| [3,4,3]×[5,3]×[&nbsp;]|| {{CDD|node|3|node|4|node|3|node|2|node|5|node|3|node|2|node}} |- |13 ||D₄A₃A₁|| [3^1,1,1]×[3,3]×[&nbsp;]|| {{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|2|node}} |- |14 ||D₄B₃A₁|| [3^1,1,1]×[4,3]×[&nbsp;]|| {{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|2|node}} |- |15 ||D₄H₃A₁|| [3^1,1,1]×[5,3]×[&nbsp;]|| {{CDD|nodes|split2|node|3|node|2|node|5|node|3|node|2|node}} |- !colspan=4|4+2+2 |- |... |- !colspan=4|4+2+1+1 |- |... |- !colspan=4|4+1+1+1+1 |- |... |- !colspan=4|3+3+2 |- !1 || A₃A₃I₂(p)||[3,3]×[3,3]×[p]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|p|node}} |- !2 || B₃A₃I₂(p)||[4,3]×[3,3]×[p]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|p|node}} |- !3 ||H₃A₃I₂(p)||[5,3]×[3,3]×[p]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|p|node}} |- !4 || B₃B₃I₂(p)||[4,3]×[4,3]×[p]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|p|node}} |- !5 ||H₃B₃I₂(p)||[5,3]×[4,3]×[p]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|p|node}} |- !6 ||H₃H₃I₂(p)||[5,3]×[5,3]×[p]||{{CDD|node|5|node|3|node|2|node|5|node|3|node|2|node|p|node}} |- !colspan=4|3+3+1+1 |- !1 || A₃²A₁²||[3,3]×[3,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|2|node}} |- !2 || B₃A₃A₁²||[4,3]×[3,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|2|node}} |- !3 ||H₃A₃A₁²||[5,3]×[3,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|2|node}} |- !4 || B₃B₃A₁²||[4,3]×[4,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|2|node}} |- !5 ||H₃B₃A₁²||[5,3]×[4,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|2|node}} |- !6 ||H₃H₃A₁²||[5,3]×[5,3]×[&nbsp;]×[&nbsp;]||{{CDD|node|5|node|3|node|2|node|5|node|3|node|2|node|2|node}} |- !colspan=4|3+2+2+1 |- |1 ||A₃I₂(p)I₂(q)A₁|| [3,3]×[p]×[q]×[&nbsp;]|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|q|node|2|node}} |- |2 ||B₃I₂(p)I₂(q)A₁|| [4,3]×[p]×[q]×[&nbsp;]|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|q|node|2|node}} |- |3 ||H₃I₂(p)I₂(q)A₁|| [5,3]×[p]×[q]×[&nbsp;]|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|q|node|2|node}} |- !colspan=4|3+2+1+1+1 |- |1 ||A₃I₂(p)A₁³|| [3,3]×[p]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|2|node|2|node}} |- |2 ||B₃I₂(p)A₁³|| [4,3]×[p]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|2|node|2|node}} |- |3 ||H₃I₂(p)A₁³|| [5,3]×[p]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|2|node|2|node}} |- !colspan=4|3+1+1+1+1+1 |- |1 ||A₃A₁⁵|| [3,3]×[&nbsp;]x[&nbsp;]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|3|node|3|node|2|node|2|node|2|node|2|node|2|node}} |- |2 ||B₃A₁⁵|| [4,3]×[&nbsp;]x[&nbsp;]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|4|node|3|node|2|node|2|node|2|node|2|node|2|node}} |- |3 ||H₃A₁⁵|| [5,3]×[&nbsp;]x[&nbsp;]×[&nbsp;]x[&nbsp;]×[&nbsp;]|| {{CDD|node|5|node|3|node|2|node|2|node|2|node|2|node|2|node}} |- !colspan=4|2+2+2+2 |- |1 ||I₂(p)I₂(q)I₂(r)I₂(s)|| [p]×[q]×[r]×[s]|| {{CDD|node|p|node|2|node|q|node|2|node|r|node|2|node|s|node}} |- !colspan=4|2+2+2+1+1 |- |1 ||I₂(p)I₂(q)I₂(r)A₁²|| [p]×[q]×[r]×[&nbsp;]×[&nbsp;]|| {{CDD|node|p|node|2|node|q|node|2|node|r|node|2|node|2|node}} |- !colspan=4|2+2+1+1+1+1 |- |2 ||I₂(p)I₂(q)A₁⁴|| [p]×[q]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|node|p|node|2|node|q|node|2|node|2|node|2|node|2|node}} |- !colspan=4|2+1+1+1+1+1+1 |- |1 ||I₂(p)A₁⁶|| [p]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|node|p|node|2|node|2|node|2|node|2|node|2|node|2|node}} |- !colspan=4|1+1+1+1+1+1+1+1 |- |1 ||A₁⁸|| [&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]×[&nbsp;]|| {{CDD|node|2|node|2|node|2|node|2|node|2|node|2|node|2|node}} |}

=== The A₈ family === The A₈ family has symmetry of order 362880 (9 [[factorial]]).

There are 135 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings (128 + 8 − 1 cases). These are all enumerated below. Bowers-style acronym names are given in parentheses for cross-referencing.

See also a [[list of 8-simplex polytopes]] for symmetric [[Coxeter plane]] graphs of these polytopes.

{| class="wikitable collapsible collapsed" !colspan=13|A₈ uniform polytopes |- !rowspan=2|# !rowspan=2|[[Coxeter-Dynkin diagram]] !rowspan=2|Truncation<BR>indices !rowspan=2|[[Norman Johnson (mathematician)|Johnson name]]<BR>(acronym){{sfn|Klitzing}} !rowspan=2|Basepoint !colspan=8|Element counts |- ! 7|| 6|| 5|| 4|| 3|| 2|| 1|| 0 |- |- align=center !1 | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}} |t₀ |[[8-simplex]] (ene) |(0,0,0,0,0,0,0,0,1) ||9 ||36 ||84 ||126 ||126 ||84 ||36 ||9 |- align=center !2 | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}} |t₁ |[[Rectified 8-simplex]] (rene) |(0,0,0,0,0,0,0,1,1) ||18 ||108 ||336 ||630 ||576 ||588 ||252 ||36 |- align=center !3 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}} |t₂ |[[Birectified 8-simplex]] (brene) |(0,0,0,0,0,0,1,1,1) ||18 ||144 ||588 ||1386 ||2016 ||1764 ||756 ||84 |- align=center !4 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}} |t₃ |[[Trirectified 8-simplex]] (trene) |(0,0,0,0,0,1,1,1,1) || || || || || || ||1260 ||126 |- align=center !5 | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1 |[[Truncated 8-simplex]] (tene) |(0,0,0,0,0,0,0,1,2) || || || || || || ||288 ||72 |- align=center !6 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t_0,2 |[[Cantellated 8-simplex]] (srene) |(0,0,0,0,0,0,1,1,2) || || || || || || ||1764 ||252 |- align=center !7 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}} |t_1,2 |[[Bitruncated 8-simplex]] (batene) |(0,0,0,0,0,0,1,2,2) || || || || || || ||1008 ||252 |- align=center !8 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t_0,3 |[[Runcinated 8-simplex]] (spene) |(0,0,0,0,0,1,1,1,2) || || || || || || ||4536 ||504 |- align=center !9 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}} |t_1,3 |[[Bicantellated 8-simplex]] (sabrene) |(0,0,0,0,0,1,1,2,2) || || || || || || ||5292 ||756 |- align=center !10 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}} |t_2,3 |[[Tritruncated 8-simplex]] (tatene) |(0,0,0,0,0,1,2,2,2) || || || || || || ||2016 ||504 |- align=center !11 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}} |t_0,4 |[[Stericated 8-simplex]] (secane) |(0,0,0,0,1,1,1,1,2) || || || || || || ||6300 ||630 |- align=center !12 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}} |t_1,4 |[[Biruncinated 8-simplex]] (sabpene) |(0,0,0,0,1,1,1,2,2) || || || || || || ||11340 ||1260 |- align=center !13 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}} |t_2,4 |[[Tricantellated 8-simplex]] (satrene) |(0,0,0,0,1,1,2,2,2) || || || || || || ||8820 ||1260 |- align=center BGCOLOR="#e0f0e0" !14 | {{dark mode invert|{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}}} |t_3,4 |[[Quadritruncated 8-simplex]] (be) |(0,0,0,0,1,2,2,2,2) || || || || || || ||2520 ||630 |- align=center !15 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}} |t_0,5 |[[Pentellated 8-simplex]] (sotane) |(0,0,0,1,1,1,1,1,2) || || || || || || ||5040 ||504 |- align=center !16 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}} |t_1,5 |[[Bistericated 8-simplex]] (sobcane) |(0,0,0,1,1,1,1,2,2) || || || || || || ||12600 ||1260 |- align=center BGCOLOR="#e0f0e0" !17 | {{dark mode invert|{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}}} |t_2,5 |[[Triruncinated 8-simplex]] (satpeb) |(0,0,0,1,1,1,2,2,2) || || || || || || ||15120 ||1680 |- align=center !18 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}} |t_0,6 |[[Hexicated 8-simplex]] (supane) |(0,0,1,1,1,1,1,1,2) || || || || || || ||2268 ||252 |- align=center BGCOLOR="#e0f0e0" !19 | {{dark mode invert|{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}}} |t_1,6 |[[Bipentellated 8-simplex]] (sobteb) |(0,0,1,1,1,1,1,2,2) || || || || || || ||7560 ||756 |- align=center BGCOLOR="#e0f0e0" !20 | {{dark mode invert|{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}}} |t_0,7 |[[Heptellated 8-simplex]] (soxeb) |(0,1,1,1,1,1,1,1,2) || || || || || || ||504 ||72 |- align=center !21 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2 |[[Cantitruncated 8-simplex]] (grene) |(0,0,0,0,0,0,1,2,3) || || || || || || ||2016 ||504 |- align=center !22 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3 |[[Runcitruncated 8-simplex]] (potane) |(0,0,0,0,0,1,1,2,3) || || || || || || ||9828 ||1512 |- align=center !23 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3 |[[Runcicantellated 8-simplex]] (prene) |(0,0,0,0,0,1,2,2,3) || || || || || || ||6804 ||1512 |- align=center !24 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3 |[[Bicantitruncated 8-simplex]] (gabrene) |(0,0,0,0,0,1,2,3,3) || || || || || || ||6048 ||1512 |- align=center !25 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4 |[[Steritruncated 8-simplex]] (catene) |(0,0,0,0,1,1,1,2,3) || || || || || || ||20160 ||2520 |- align=center !26 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t_0,2,4 |[[Stericantellated 8-simplex]] (crane) |(0,0,0,0,1,1,2,2,3) |2| || || || || || ||26460 ||3780 |- align=center !27 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t_1,2,4 |[[Biruncitruncated 8-simplex]] (biptene) |(0,0,0,0,1,1,2,3,3) || || || || || || ||22680 ||3780 |- align=center !28 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t_0,3,4 |[[Steriruncinated 8-simplex]] (capene) |(0,0,0,0,1,2,2,2,3) || || || || || || ||12600 ||2520 |- align=center !29 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}} |t_1,3,4 |[[Biruncicantellated 8-simplex]] (biprene) |(0,0,0,0,1,2,2,3,3) || || || || || || ||18900 ||3780 |- align=center !30 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}} |t_2,3,4 |[[Tricantitruncated 8-simplex]] (gatrene) |(0,0,0,0,1,2,3,3,3) || || || || || || ||10080 ||2520 |- align=center !31 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1,5 |[[Pentitruncated 8-simplex]] (tetane) |(0,0,0,1,1,1,1,2,3) || || || || || || ||21420 ||2520 |- align=center !32 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} |t_0,2,5 |[[Penticantellated 8-simplex]] (turane) |(0,0,0,1,1,1,2,2,3) || || || || || || ||42840 ||5040 |- align=center !33 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}} |t_1,2,5 |[[Bisteritruncated 8-simplex]] (bictane) |(0,0,0,1,1,1,2,3,3) || || || || || || ||35280 ||5040 |- align=center !34 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}} |t_0,3,5 |[[Pentiruncinated 8-simplex]] (topene) |(0,0,0,1,1,2,2,2,3) || || || || || || ||37800 ||5040 |- align=center !35 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}} |t_1,3,5 |[[Bistericantellated 8-simplex]] (bocrane) |(0,0,0,1,1,2,2,3,3) || || || || || || ||52920 ||7560 |- align=center !36 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}} |t_2,3,5 |[[Runcinated 8-simplexes#Triruncitruncated 8-simplex|Triruncitruncated 8-simplex]] (toprane) |(0,0,0,1,1,2,3,3,3) || || || || || || ||27720 ||5040 |- align=center !37 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}} |t_0,4,5 |[[Pentistericated 8-simplex]] (tecane) |(0,0,0,1,2,2,2,2,3) || || || || || || ||13860 ||2520 |- align=center !38 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}} |t_1,4,5 |[[Bisteriruncinated 8-simplex]] (bacpane) |(0,0,0,1,2,2,2,3,3) || || || || || || ||30240 ||5040 |- align=center !39 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1,6 |[[Hexitruncated 8-simplex]] (putene) |(0,0,1,1,1,1,1,2,3) || || || || || || ||12096 ||1512 |- align=center !40 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t_0,2,6 |[[Hexicantellated 8-simplex]] (purene) |(0,0,1,1,1,1,2,2,3) || || || || || || ||34020 ||3780 |- align=center !41 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}} |t_1,2,6 |[[Bipentitruncated 8-simplex]] (bitotene) |(0,0,1,1,1,1,2,3,3) || || || || || || ||26460 ||3780 |- align=center !42 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t_0,3,6 |[[Hexiruncinated 8-simplex]] (pupene) |(0,0,1,1,1,2,2,2,3) || || || || || || ||45360 ||5040 |- align=center !43 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}} |t_1,3,6 |[[Bipenticantellated 8-simplex]] (bitrene) |(0,0,1,1,1,2,2,3,3) || || || || || || ||60480 ||7560 |- align=center !44 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}} |t_0,4,6 |[[Hexistericated 8-simplex]] (pucane) |(0,0,1,1,2,2,2,2,3) || || || || || || ||30240 ||3780 |- align=center !45 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}} |t_0,5,6 |[[Hexipentellated 8-simplex]] (putane) |(0,0,1,2,2,2,2,2,3) || || || || || || ||9072 ||1512 |- align=center !46 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1,7 |[[Heptitruncated 8-simplex]] (xotane) |(0,1,1,1,1,1,1,2,3) || || || || || || ||3276 ||504 |- align=center !47 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t_0,2,7 |[[Hepticantellated 8-simplex]] (xorene){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/xorene.htm (x3o3x3o3o3o3o3x3 - xorene)]}} |(0,1,1,1,1,1,2,2,3) || || || || || || ||12852 ||1512 |- align=center !48 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t_0,3,7 |[[Heptiruncinated 8-simplex]] (xapane) |(0,1,1,1,1,2,2,2,3) || || || || || || ||23940 ||2520 |- align=center !49 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3 |[[Runcicantitruncated 8-simplex]] (gapene) |(0,0,0,0,0,1,2,3,4) || || || || || || ||12096 ||3024 |- align=center !50 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4 |[[Stericantitruncated 8-simplex]] (cograne) |(0,0,0,0,1,1,2,3,4) || || || || || || ||45360 ||7560 |- align=center !51 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4 |[[Steriruncitruncated 8-simplex]] (coptane) |(0,0,0,0,1,2,2,3,4) || || || || || || ||34020 ||7560 |- align=center !52 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,4 |[[Steriruncicantellated 8-simplex]] (coprene) |(0,0,0,0,1,2,3,3,4) || || || || || || ||34020 ||7560 |- align=center !53 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,4 |[[Biruncicantitruncated 8-simplex]] (gabpene) |(0,0,0,0,1,2,3,4,4) || || || || || || ||30240 ||7560 |- align=center !54 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,5 |[[Penticantitruncated 8-simplex]] (tograne) |(0,0,0,1,1,1,2,3,4) || || || || || || ||70560 ||10080 |- align=center !55 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,5 |[[Pentiruncitruncated 8-simplex]] (taptane) |(0,0,0,1,1,2,2,3,4) || || || || || || ||98280 ||15120 |- align=center !56 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,5 |[[Pentiruncicantellated 8-simplex]] (taprene) |(0,0,0,1,1,2,3,3,4) || || || || || || ||90720 ||15120 |- align=center !57 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,5 |[[Bistericantitruncated 8-simplex]] (bocagrane) |(0,0,0,1,1,2,3,4,4) || || || || || || ||83160 ||15120 |- align=center !58 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4,5 |[[Pentisteritruncated 8-simplex]] (tectane) |(0,0,0,1,2,2,2,3,4) || || || || || || ||50400 ||10080 |- align=center !59 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t_0,2,4,5 |[[Pentistericantellated 8-simplex]] (tocrane) |(0,0,0,1,2,2,3,3,4) || || || || || || ||83160 ||15120 |- align=center !60 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t_1,2,4,5 |[[Bisteriruncitruncated 8-simplex]] (bicpotane) |(0,0,0,1,2,2,3,4,4) || || || || || || ||68040 ||15120 |- align=center !61 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t_0,3,4,5 |[[Pentisteriruncinated 8-simplex]] (tecpane) |(0,0,0,1,2,3,3,3,4) || || || || || || ||50400 ||10080 |- align=center !62 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}} |t_1,3,4,5 |[[Bisteriruncicantellated 8-simplex]] (bicprene) |(0,0,0,1,2,3,3,4,4) || || || || || || ||75600 ||15120 |- align=center BGCOLOR="#e0f0e0" !63 | {{dark mode invert|{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}}} |t_2,3,4,5 |[[Triruncicantitruncated 8-simplex]] (gatpeb) |(0,0,0,1,2,3,4,4,4) || || || || || || ||40320 ||10080 |- align=center !64 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,6 |[[Hexicantitruncated 8-simplex]] (pugrane) |(0,0,1,1,1,1,2,3,4) || || || || || || ||52920 ||7560 |- align=center !65 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,6 |[[Hexiruncitruncated 8-simplex]] (puptane) |(0,0,1,1,1,2,2,3,4) || || || || || || ||113400 ||15120 |- align=center !66 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,6 |[[Hexiruncicantellated 8-simplex]] (puprene) |(0,0,1,1,1,2,3,3,4) || || || || || || ||98280 ||15120 |- align=center !67 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,6 |[[Bipenticantitruncated 8-simplex]] (batograne) |(0,0,1,1,1,2,3,4,4) || || || || || || ||90720 ||15120 |- align=center !68 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4,6 |[[Hexisteritruncated 8-simplex]] (puctane) |(0,0,1,1,2,2,2,3,4) || || || || || || ||105840 ||15120 |- align=center !69 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t_0,2,4,6 |[[Hexistericantellated 8-simplex]] (pucrene) |(0,0,1,1,2,2,3,3,4) || || || || || || ||158760 ||22680 |- align=center !70 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t_1,2,4,6 |[[Bipentiruncitruncated 8-simplex]] (batpitane) |(0,0,1,1,2,2,3,4,4) || || || || || || ||136080 ||22680 |- align=center !71 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t_0,3,4,6 |[[Hexisteriruncinated 8-simplex]] (pocapine) |(0,0,1,1,2,3,3,3,4) || || || || || || ||90720 ||15120 |- align=center BGCOLOR="#e0f0e0" !72 | {{dark mode invert|{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}}} |t_1,3,4,6 |[[Bipentiruncicantellated 8-simplex]] (bitprop) |(0,0,1,1,2,3,3,4,4) || || || || || || ||136080 ||22680 |- align=center !73 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1,5,6 |[[Hexipentitruncated 8-simplex]] (putatine) |(0,0,1,2,2,2,2,3,4) || || || || || || ||41580 ||7560 |- align=center !74 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} |t_0,2,5,6 |[[Hexipenticantellated 8-simplex]] (putarene) |(0,0,1,2,2,2,3,3,4) || || || || || || ||98280 ||15120 |- align=center BGCOLOR="#e0f0e0" !75 | {{dark mode invert|{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}}} |t_1,2,5,6 |[[Bipentisteritruncated 8-simplex]] (batcotab) |(0,0,1,2,2,2,3,4,4) || || || || || || ||75600 ||15120 |- align=center !76 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}} |t_0,3,5,6 |[[Hexipentiruncinated 8-simplex]] (putapene) |(0,0,1,2,2,3,3,3,4) || || || || || || ||98280 ||15120 |- align=center !77 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}} |t_0,4,5,6 |[[Hexipentistericated 8-simplex]] (putacane) |(0,0,1,2,3,3,3,3,4) || || || || || || ||41580 ||7560 |- align=center !78 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,7 |[[Hepticantitruncated 8-simplex]] (xograne) |(0,1,1,1,1,1,2,3,4) || || || || || || ||18144 ||3024 |- align=center !79 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,7 |[[Heptiruncitruncated 8-simplex]] (xaptane) |(0,1,1,1,1,2,2,3,4) || || || || || || ||56700 ||7560 |- align=center !80 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,7 |[[Heptiruncicantellated 8-simplex]] (xeprane) |(0,1,1,1,1,2,3,3,4) || || || || || || ||45360 ||7560 |- align=center !81 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4,7 |[[Heptisteritruncated 8-simplex]] (xactane) |(0,1,1,1,2,2,2,3,4) || || || || || || ||80640 ||10080 |- align=center !82 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t_0,2,4,7 |[[Heptistericantellated 8-simplex]] (xacrene) |(0,1,1,1,2,2,3,3,4) || || || || || || ||113400 ||15120 |- align=center BGCOLOR="#e0f0e0" !83 | {{dark mode invert|{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}}} |t_0,3,4,7 |[[Heptisteriruncinated 8-simplex]] (xocapob) |(0,1,1,1,2,3,3,3,4) || || || || || || ||60480 ||10080 |- align=center !84 | {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t_0,1,5,7 |[[Heptipentitruncated 8-simplex]] (xotatine) |(0,1,1,2,2,2,2,3,4) || || || || || || ||56700 ||7560 |- align=center BGCOLOR="#e0f0e0" !85 | {{dark mode invert|{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}}} |t_0,2,5,7 |[[Heptipenticantellated 8-simplex]] (xotrab) |(0,1,1,2,2,2,3,3,4) || || || || || || ||120960 ||15120 |- align=center BGCOLOR="#e0f0e0" !86 | {{dark mode invert|{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}}} |t_0,1,6,7 |[[Heptihexitruncated 8-simplex]] (xupatab) |(0,1,2,2,2,2,2,3,4) || || || || || || ||18144 ||3024 |- align=center !87 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,4 |[[Steriruncicantitruncated 8-simplex]] (gacene) |(0,0,0,0,1,2,3,4,5) || || || || || || ||60480 ||15120 |- align=center !88 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,5 |[[Pentiruncicantitruncated 8-simplex]] (togapene) |(0,0,0,1,1,2,3,4,5) || || || || || || ||166320 ||30240 |- align=center !89 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,5 |[[Pentistericantitruncated 8-simplex]] (tecograne) |(0,0,0,1,2,2,3,4,5) || || || || || || ||136080 ||30240 |- align=center !90 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4,5 |[[Pentisteriruncitruncated 8-simplex]] (tecpatane) |(0,0,0,1,2,3,3,4,5) || || || || || || ||136080 ||30240 |- align=center !91 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,4,5 |[[Pentisteriruncicantellated 8-simplex]] (ticprane) |(0,0,0,1,2,3,4,4,5) || || || || || || ||136080 ||30240 |- align=center !92 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,4,5 |[[Bisteriruncicantitruncated 8-simplex]] (gobcane) |(0,0,0,1,2,3,4,5,5) || || || || || || ||120960 ||30240 |- align=center !93 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,6 |[[Hexiruncicantitruncated 8-simplex]] (pogapene) |(0,0,1,1,1,2,3,4,5) || || || || || || ||181440 ||30240 |- align=center !94 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,6 |[[Hexistericantitruncated 8-simplex]] (pocagrane) |(0,0,1,1,2,2,3,4,5) || || || || || || ||272160 ||45360 |- align=center !95 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4,6 |[[Hexisteriruncitruncated 8-simplex]] (pocpatine) |(0,0,1,1,2,3,3,4,5) || || || || || || ||249480 ||45360 |- align=center !96 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,4,6 |[[Hexisteriruncicantellated 8-simplex]] (pocpurene) |(0,0,1,1,2,3,4,4,5) || || || || || || ||249480 ||45360 |- align=center !97 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,4,6 |[[Bipentiruncicantitruncated 8-simplex]] (botagpane) |(0,0,1,1,2,3,4,5,5) || || || || || || ||226800 ||45360 |- align=center !98 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,5,6 |[[Hexipenticantitruncated 8-simplex]] (potagrene) |(0,0,1,2,2,2,3,4,5) || || || || || || ||151200 ||30240 |- align=center !99 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,5,6 |[[Hexipentiruncitruncated 8-simplex]] (potaptane) |(0,0,1,2,2,3,3,4,5) || || || || || || ||249480 ||45360 |- align=center !100 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,5,6 |[[Hexipentiruncicantellated 8-simplex]] (putaprene) |(0,0,1,2,2,3,4,4,5) || || || || || || ||226800 ||45360 |- align=center !101 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t_1,2,3,5,6 |[[Bipentistericantitruncated 8-simplex]] (betcagrane) |(0,0,1,2,2,3,4,5,5) || || || || || || ||204120 ||45360 |- align=center !102 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4,5,6 |[[Hexipentisteritruncated 8-simplex]] (putcatine) |(0,0,1,2,3,3,3,4,5) || || || || || || ||151200 ||30240 |- align=center !103 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t_0,2,4,5,6 |[[Hexipentistericantellated 8-simplex]] (potacrane) |(0,0,1,2,3,3,4,4,5) || || || || || || ||249480 ||45360 |- align=center !104 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t_0,3,4,5,6 |[[Hexipentisteriruncinated 8-simplex]] (potcapane) |(0,0,1,2,3,4,4,4,5) || || || || || || ||151200 ||30240 |- align=center !105 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,7 |[[Heptiruncicantitruncated 8-simplex]] (xigpane) |(0,1,1,1,1,2,3,4,5) || || || || || || ||83160 ||15120 |- align=center !106 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,7 |[[Heptistericantitruncated 8-simplex]] (xecagrane) |(0,1,1,1,2,2,3,4,5) || || || || || || ||196560 ||30240 |- align=center !107 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4,7 |[[Heptisteriruncitruncated 8-simplex]] (xucaptane) |(0,1,1,1,2,3,3,4,5) || || || || || || ||166320 ||30240 |- align=center !108 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,4,7 |[[Heptisteriruncicantellated 8-simplex]] (xecaprane) |(0,1,1,1,2,3,4,4,5) || || || || || || ||166320 ||30240 |- align=center !109 | {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,5,7 |[[Heptipenticantitruncated 8-simplex]] (xotagrane) |(0,1,1,2,2,2,3,4,5) || || || || || || ||196560 ||30240 |- align=center !110 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,5,7 |[[Heptipentiruncitruncated 8-simplex]] (xitaptene) |(0,1,1,2,2,3,3,4,5) || || || || || || ||294840 ||45360 |- align=center !111 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,5,7 |[[Heptipentiruncicantellated 8-simplex]] (xataprane) |(0,1,1,2,2,3,4,4,5) || || || || || || ||272160 ||45360 |- align=center !112 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t_0,1,4,5,7 |[[Heptipentisteritruncated 8-simplex]] (xotcatene) |(0,1,1,2,3,3,3,4,5) || || || || || || ||166320 ||30240 |- align=center !113 | {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,6,7 |[[Heptihexicantitruncated 8-simplex]] (xopugrane) |(0,1,2,2,2,2,3,4,5) || || || || || || ||83160 ||15120 |- align=center !114 | {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,6,7 |[[Heptihexiruncitruncated 8-simplex]] (xopupatane) |(0,1,2,2,2,3,3,4,5) || || || || || || ||196560 ||30240 |- align=center !115 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,4,5 |[[Pentisteriruncicantitruncated 8-simplex]] (gotane) |(0,0,0,1,2,3,4,5,6) || || || || || || ||241920 ||60480 |- align=center !116 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,4,6 |[[Hexisteriruncicantitruncated 8-simplex]] (pogacane) |(0,0,1,1,2,3,4,5,6) || || || || || || ||453600 ||90720 |- align=center !117 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,5,6 |[[Hexipentiruncicantitruncated 8-simplex]] (potegpane) |(0,0,1,2,2,3,4,5,6) || || || || || || ||408240 ||90720 |- align=center !118 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,5,6 |[[Hexipentistericantitruncated 8-simplex]] (potacagrane) |(0,0,1,2,3,3,4,5,6) || || || || || || ||408240 ||90720 |- align=center !119 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4,5,6 |[[Hexipentisteriruncitruncated 8-simplex]] (poticaptine) |(0,0,1,2,3,4,4,5,6) || || || || || || ||408240 ||90720 |- align=center !120 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t_0,2,3,4,5,6 |[[Hexipentisteriruncicantellated 8-simplex]] (poticoprane) |(0,0,1,2,3,4,5,5,6) || || || || || || ||408240 ||90720 |- align=center BGCOLOR="#e0f0e0" !121 | {{dark mode invert|{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}} |t_1,2,3,4,5,6 |[[Bipentisteriruncicantitruncated 8-simplex]] (gobteb) |(0,0,1,2,3,4,5,6,6) || || || || || || ||362880 ||90720 |- align=center !122 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,4,7 |[[Heptisteriruncicantitruncated 8-simplex]] (xogacane) |(0,1,1,1,2,3,4,5,6) || || || || || || ||302400 ||60480 |- align=center !123 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,5,7 |[[Heptipentiruncicantitruncated 8-simplex]] (xotagapane) |(0,1,1,2,2,3,4,5,6) || || || || || || ||498960 ||90720 |- align=center !124 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,5,7 |[[Heptipentistericantitruncated 8-simplex]] (xotcagrane) |(0,1,1,2,3,3,4,5,6) || || || || || || ||453600 ||90720 |- align=center !125 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t_0,1,3,4,5,7 |[[Heptipentisteriruncitruncated 8-simplex]] (xotacaptane) |(0,1,1,2,3,4,4,5,6) || || || || || || ||453600 ||90720 |- align=center BGCOLOR="#e0f0e0" !126 | {{dark mode invert|{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}} |t_0,2,3,4,5,7 |[[Heptipentisteriruncicantellated 8-simplex]] (xotacaparb) |(0,1,1,2,3,4,5,5,6) || || || || || || ||453600 ||90720 |- align=center !127 | {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_0,1,2,3,6,7 |[[Heptihexiruncicantitruncated 8-simplex]] (xupogapene) |(0,1,2,2,2,3,4,5,6) || || || || || || ||302400 ||60480 |- align=center !128 | {{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t_0,1,2,4,6,7 |[[Heptihexistericantitruncated 8-simplex]] (xupcagrene) |(0,1,2,2,3,3,4,5,6) || || || || || || ||498960 ||90720 |- align=center BGCOLOR="#e0f0e0" !129 | {{dark mode invert|{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}} |t_0,1,3,4,6,7 |[[Heptihexisteriruncitruncated 8-simplex]] (xupacputob) |(0,1,2,2,3,4,4,5,6) || || || || || || ||453600 ||90720 |- align=center BGCOLOR="#e0f0e0" !130 | {{dark mode invert|{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}}} |t_0,1,2,5,6,7 |[[Heptihexipenticantitruncated 8-simplex]] (xuptagrab) |(0,1,2,3,3,3,4,5,6) || || || || || || ||302400 ||60480 |- align=center !131 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_{0,1,2,3,4,5,6} |[[Hexipentisteriruncicantitruncated 8-simplex]] (gupane) |(0,0,1,2,3,4,5,6,7) || || || || || || ||725760 ||181440 |- align=center !132 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_{0,1,2,3,4,5,7} |[[Heptipentisteriruncicantitruncated 8-simplex]] (xogtane) |(0,1,1,2,3,4,5,6,7) || || || || || || ||816480 ||181440 |- align=center !133 | {{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t_{0,1,2,3,4,6,7} |[[Heptihexisteriruncicantitruncated 8-simplex]] (xupogacane) |(0,1,2,2,3,4,5,6,7) || || || || || || ||816480 ||181440 |- align=center !134 | {{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t_{0,1,2,3,5,6,7} |[[Heptihexipentiruncicantitruncated 8-simplex]] (xuptagapene) |(0,1,2,3,3,4,5,6,7) || || || || || || ||816480 ||181440 |- align=center BGCOLOR="#e0f0e0" !135 | {{dark mode invert|{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}} |t_{0,1,2,3,4,5,6,7} |[[Omnitruncated 8-simplex]] (goxeb) |(0,1,2,3,4,5,6,7,8) || || || || || || ||1451520 ||362880 |}

=== The B₈ family === The B₈ family has symmetry of order 10321920 (8 [[factorial]] × 2⁸). There are 255 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings.

See also a [[list of B8 polytopes]] for symmetric [[Coxeter plane]] graphs of these polytopes.

{| class="wikitable collapsible collapsed" !colspan=13|B₈ uniform polytopes |- !rowspan=2|# !rowspan=2|[[Coxeter-Dynkin diagram]] !rowspan=2|[[Schläfli symbol|Schläfli<BR>symbol]] !rowspan=2|Name !colspan=8|Element counts |- ! 7|| 6|| 5|| 4|| 3|| 2|| 1|| 0 |- align=center BGCOLOR="#f0e0e0" !1 |<!-- [x3o3o3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}}}||t₀{3⁶,4}||[[8-orthoplex]]<BR>Diacosipentacontahexazetton (ek)||256||1024||1792||1792||1120||448||112||16 |- align=center BGCOLOR="#f0e0e0" !2 |<!-- [o3x3o3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}}}||t₁{3⁶,4}||[[Rectified 8-orthoplex]]<BR>Rectified diacosipentacontahexazetton (rek)||272||3072||8960||12544||10080||4928||1344||112 |- align=center BGCOLOR="#f0e0e0" !3 |<!-- [o3o3x3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}}}||t₂{3⁶,4}||[[Birectified 8-orthoplex]]<BR>Birectified diacosipentacontahexazetton (bark)||272||3184||16128||34048||36960||22400||6720||448 |- align=center BGCOLOR="#f0e0e0" !4 |<!-- [o3o3o3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}}}||t₃{3⁶,4}||[[Trirectified 8-orthoplex]]<BR>Trirectified diacosipentacontahexazetton (tark)||272||3184||16576||48384||71680||53760||17920||1120 |- align=center BGCOLOR="#e0e0f0" !5 |<!-- [o3o3o3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}}}||t₃{4,3⁶}||[[Trirectified 8-cube]]<BR>Trirectified octeract (tro)||272||3184||16576||47712||80640||71680||26880||1792 |- align=center BGCOLOR="#e0e0f0" !6 |<!-- [o3o3o3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}}}||t₂{4,3⁶}||[[Birectified 8-cube]]<BR>Birectified octeract (bro)||272||3184||14784||36960||55552||50176||21504||1792 |- align=center BGCOLOR="#e0e0f0" !7 |<!-- [o3o3o3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}}}||t₁{4,3⁶}||[[Rectified 8-cube]]<BR>Rectified octeract (recto)||272||2160||7616||15456||19712||16128||7168||1024 |- align=center BGCOLOR="#e0e0f0" !8 |<!-- [o3o3o3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}}}||t₀{4,3⁶}||[[8-cube]]<BR>Octeract (octo)||16||112||448||1120||1792||1792||1024||256 |- align=center BGCOLOR="#f0e0e0" !9 |<!-- [x3x3o3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1{3⁶,4}||[[Truncated 8-orthoplex]]<BR>Truncated diacosipentacontahexazetton (tek)||||||||||||||1456||224 |- align=center BGCOLOR="#f0e0e0" !10 |<!-- [x3o3x3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2{3⁶,4}||Cantellated 8-orthoplex{{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/srek.htm x3o3x3o3o3o3o4o - srek]}} <BR>Small rhombated diacosipentacontahexazetton (srek)||||||||||||||14784||1344 |- align=center BGCOLOR="#f0e0e0" !11 |<!-- [o3x3x3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2{3⁶,4}||[[Bitruncated 8-orthoplex]]<BR>Bitruncated diacosipentacontahexazetton (batek)||||||||||||||8064||1344 |- align=center BGCOLOR="#f0e0e0" !12 |<!-- [x3o3o3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3{3⁶,4}||[[Runcinated 8-orthoplex]]<BR>Small prismated diacosipentacontahexazetton (spek)||||||||||||||60480||4480 |- align=center BGCOLOR="#f0e0e0" !13 |<!-- [o3x3o3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3{3⁶,4}||[[Bicantellated 8-orthoplex]]<BR>Small birhombated diacosipentacontahexazetton (sabork)||||||||||||||67200||6720 |- align=center BGCOLOR="#f0e0e0" !14 |<!-- [o3o3x3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_2,3{3⁶,4}||[[Tritruncated 8-orthoplex]]<BR>Tritruncated diacosipentacontahexazetton (tatek)||||||||||||||24640||4480 |- align=center BGCOLOR="#f0e0e0" !15 |<!-- [x3o3o3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,4{3⁶,4}||[[Stericated 8-orthoplex]]<BR>Small cellated diacosipentacontahexazetton (scak)||||||||||||||125440||8960 |- align=center BGCOLOR="#f0e0e0" !16 |<!-- [o3x3o3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_1,4{3⁶,4}||[[Biruncinated 8-orthoplex]]<BR>Small biprismated diacosipentacontahexazetton (sabpek)||||||||||||||215040||17920 |- align=center BGCOLOR="#f0e0e0" !17 |<!-- [o3o3x3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_2,4{3⁶,4}||[[Tricantellated 8-orthoplex]]<BR>Small trirhombated diacosipentacontahexazetton (satrek)||||||||||||||161280||17920 |- align=center BGCOLOR="#e0f0e0" !18 |<!-- [o3o3o3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_3,4{4,3⁶}||[[Quadritruncated 8-cube]]<BR>Octeractidiacosipentacontahexazetton (oke)||||||||||||||44800||8960 |- align=center BGCOLOR="#f0e0e0" !19 |<!-- [x3o3o3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,5{3⁶,4}||[[Pentellated 8-orthoplex]]<BR>Small terated diacosipentacontahexazetton (setek)||||||||||||||134400||10752 |- align=center BGCOLOR="#f0e0e0" !20 |<!-- [o3x3o3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}}}||t_1,5{3⁶,4}||[[Bistericated 8-orthoplex]]<BR>Small bicellated diacosipentacontahexazetton (sibcak)||||||||||||||322560||26880 |- align=center BGCOLOR="#e0f0e0" !21 |<!-- [o3o3x3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}}}||t_2,5{4,3⁶}||[[Triruncinated 8-cube]]<BR>Small triprismato-octeractidiacosipentacontahexazetton (sitpoke)||||||||||||||376320||35840 |- align=center BGCOLOR="#e0e0f0" !22 |<!-- [o3o3o3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}}}||t_2,4{4,3⁶}||[[Tricantellated 8-cube]]<BR>Small trirhombated octeract (satro)||||||||||||||215040||26880 |- align=center BGCOLOR="#e0e0f0" !23 |<!-- [o3o3o3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}}}||t_2,3{4,3⁶}||[[Tritruncated 8-cube]]<BR>Tritruncated octeract (tato)||||||||||||||48384||10752 |- align=center BGCOLOR="#f0e0e0" !24 |<!-- [x3o3o3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,6{3⁶,4}||[[Hexicated 8-orthoplex]]<BR>Small petated diacosipentacontahexazetton (supek)||||||||||||||64512||7168 |- align=center BGCOLOR="#e0f0e0" !25 |<!-- [o3x3o3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}}}||t_1,6{4,3⁶}||[[Bipentellated 8-cube]]<BR>Small biteri-octeractidiacosipentacontahexazetton (sabtoke)||||||||||||||215040||21504 |- align=center BGCOLOR="#e0e0f0" !26 |<!-- [o3o3x3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}}}||t_1,5{4,3⁶}||[[Bistericated 8-cube]]<BR>Small bicellated octeract (sobco)||||||||||||||358400||35840 |- align=center BGCOLOR="#e0e0f0" !27 |<!-- [o3o3o3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}}}||t_1,4{4,3⁶}||[[Biruncinated 8-cube]]<BR>Small biprismated octeract (sabepo)||||||||||||||322560||35840 |- align=center BGCOLOR="#e0e0f0" !28 |<!-- [o3o3o3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}}}||t_1,3{4,3⁶}||[[Bicantellated 8-cube]]<BR>Small birhombated octeract (subro)||||||||||||||150528||21504 |- align=center BGCOLOR="#e0e0f0" !29 |<!-- [o3o3o3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}}}||t_1,2{4,3⁶}||[[Bitruncated 8-cube]]<BR>Bitruncated octeract (bato)||||||||||||||28672||7168 |- align=center BGCOLOR="#e0f0e0" !30 |<!-- [x3o3o3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,7{4,3⁶}||[[Heptellated 8-cube]]<BR>Small exi-octeractidiacosipentacontahexazetton (saxoke)||||||||||||||14336||2048 |- align=center BGCOLOR="#e0e0f0" !31 |<!-- [o3x3o3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}}}||t_0,6{4,3⁶}||[[Hexicated 8-cube]]<BR>Small petated octeract (supo)||||||||||||||64512||7168 |- align=center BGCOLOR="#e0e0f0" !32 |<!-- [o3o3x3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}}}||t_0,5{4,3⁶}||[[Pentellated 8-cube]]<BR>Small terated octeract (soto)||||||||||||||143360||14336 |- align=center BGCOLOR="#e0e0f0" !33 |<!-- [o3o3o3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}}}||t_0,4{4,3⁶}||[[Stericated 8-cube]]<BR>Small cellated octeract (soco)||||||||||||||179200||17920 |- align=center BGCOLOR="#e0e0f0" !34 |<!-- [o3o3o3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}}}||t_0,3{4,3⁶}||[[Runcinated 8-cube]]<BR>Small prismated octeract (sopo)||||||||||||||129024||14336 |- align=center BGCOLOR="#e0e0f0" !35 |<!-- [o3o3o3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}}}||t_0,2{4,3⁶}||[[Cantellated 8-cube]]<BR>Small rhombated octeract (soro)||||||||||||||50176||7168 |- align=center BGCOLOR="#e0e0f0" !36 |<!-- [o3o3o3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}}}||t_0,1{4,3⁶}||[[Truncated 8-cube]]<BR>Truncated octeract (tocto)||||||||||||||8192||2048 |- align=center BGCOLOR="#f0e0e0" !37 |<!-- [x3x3x3o3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2{3⁶,4}||[[Cantitruncated 8-orthoplex]]<BR>Great rhombated diacosipentacontahexazetton||||||||||||||16128||2688 |- align=center BGCOLOR="#f0e0e0" !38 |<!-- [x3x3o3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3{3⁶,4}||[[Runcitruncated 8-orthoplex]]<BR>Prismatotruncated diacosipentacontahexazetton||||||||||||||127680||13440 |- align=center BGCOLOR="#f0e0e0" !39 |<!-- [x3o3x3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3{3⁶,4}||[[Runcicantellated 8-orthoplex]]<BR>Prismatorhombated diacosipentacontahexazetton||||||||||||||80640||13440 |- align=center BGCOLOR="#f0e0e0" !40 |<!-- [o3x3x3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3{3⁶,4}||[[Bicantitruncated 8-orthoplex]]<BR>Great birhombated diacosipentacontahexazetton||||||||||||||73920||13440 |- align=center BGCOLOR="#f0e0e0" !41 |<!-- [x3x3o3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4{3⁶,4}||[[Steritruncated 8-orthoplex]]<BR>Cellitruncated diacosipentacontahexazetton||||||||||||||394240||35840 |- align=center BGCOLOR="#f0e0e0" !42 |<!-- [x3o3x3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,4{3⁶,4}||[[Stericantellated 8-orthoplex]]<BR>Cellirhombated diacosipentacontahexazetton||||||||||||||483840||53760 |- align=center BGCOLOR="#f0e0e0" !43 |<!-- [o3x3x3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,4{3⁶,4}||[[Biruncitruncated 8-orthoplex]]<BR>Biprismatotruncated diacosipentacontahexazetton||||||||||||||430080||53760 |- align=center BGCOLOR="#f0e0e0" !44 |<!-- [x3o3o3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,4{3⁶,4}||[[Steriruncinated 8-orthoplex]]<BR>Celliprismated diacosipentacontahexazetton||||||||||||||215040||35840 |- align=center BGCOLOR="#f0e0e0" !45 |<!-- [o3x3o3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3,4{3⁶,4}||[[Biruncicantellated 8-orthoplex]]<BR>Biprismatorhombated diacosipentacontahexazetton||||||||||||||322560||53760 |- align=center BGCOLOR="#f0e0e0" !46 |<!-- [o3o3x3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_2,3,4{3⁶,4}||[[Tricantitruncated 8-orthoplex]]<BR>Great trirhombated diacosipentacontahexazetton||||||||||||||179200||35840 |- align=center BGCOLOR="#f0e0e0" !47 |<!-- [x3x3o3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,5{3⁶,4}||[[Pentitruncated 8-orthoplex]]<BR>Teritruncated diacosipentacontahexazetton||||||||||||||564480||53760 |- align=center BGCOLOR="#f0e0e0" !48 |<!-- [x3o3x3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,5{3⁶,4}||[[Penticantellated 8-orthoplex]]<BR>Terirhombated diacosipentacontahexazetton||||||||||||||1075200||107520 |- align=center BGCOLOR="#f0e0e0" !49 |<!-- [o3x3x3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,5{3⁶,4}||[[Bisteritruncated 8-orthoplex]]<BR>Bicellitruncated diacosipentacontahexazetton||||||||||||||913920||107520 |- align=center BGCOLOR="#f0e0e0" !50 |<!-- [x3o3o3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,5{3⁶,4}||[[Pentiruncinated 8-orthoplex]]<BR>Teriprismated diacosipentacontahexazetton||||||||||||||913920||107520 |- align=center BGCOLOR="#f0e0e0" !51 |<!-- [o3x3o3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3,5{3⁶,4}||[[Bistericantellated 8-orthoplex]]<BR>Bicellirhombated diacosipentacontahexazetton||||||||||||||1290240||161280 |- align=center BGCOLOR="#f0e0e0" !52 |<!-- [o3o3x3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_2,3,5{3⁶,4}||[[Triruncitruncated 8-orthoplex]]<BR>Triprismatotruncated diacosipentacontahexazetton||||||||||||||698880||107520 |- align=center BGCOLOR="#f0e0e0" !53 |<!-- [x3o3o3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,4,5{3⁶,4}||[[Pentistericated 8-orthoplex]]<BR>Tericellated diacosipentacontahexazetton||||||||||||||322560||53760 |- align=center BGCOLOR="#f0e0e0" !54 |<!-- [o3x3o3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_1,4,5{3⁶,4}||[[Bisteriruncinated 8-orthoplex]]<BR>Bicelliprismated diacosipentacontahexazetton||||||||||||||698880||107520 |- align=center BGCOLOR="#e0e0f0" !55 |<!-- [o3o3x3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_2,3,5{4,3⁶}||[[Triruncitruncated 8-cube]]<BR>Triprismatotruncated octeract||||||||||||||645120||107520 |- align=center BGCOLOR="#e0e0f0" !56 |<!-- [o3o3o3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_2,3,4{4,3⁶}||[[Tricantitruncated 8-cube]]<BR>Great trirhombated octeract||||||||||||||241920||53760 |- align=center BGCOLOR="#f0e0e0" !57 |<!-- [x3x3o3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,6{3⁶,4}||[[Hexitruncated 8-orthoplex]]<BR>Petitruncated diacosipentacontahexazetton||||||||||||||344064||43008 |- align=center BGCOLOR="#f0e0e0" !58 |<!-- [x3o3x3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,6{3⁶,4}||[[Hexicantellated 8-orthoplex]]<BR>Petirhombated diacosipentacontahexazetton||||||||||||||967680||107520 |- align=center BGCOLOR="#f0e0e0" !59 |<!-- [o3x3x3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,6{3⁶,4}||[[Bipentitruncated 8-orthoplex]]<BR>Biteritruncated diacosipentacontahexazetton||||||||||||||752640||107520 |- align=center BGCOLOR="#f0e0e0" !60 |<!-- [x3o3o3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,6{3⁶,4}||[[Hexiruncinated 8-orthoplex]]<BR>Petiprismated diacosipentacontahexazetton||||||||||||||1290240||143360 |- align=center BGCOLOR="#f0e0e0" !61 |<!-- [o3x3o3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3,6{3⁶,4}||[[Bipenticantellated 8-orthoplex]]<BR>Biterirhombated diacosipentacontahexazetton||||||||||||||1720320||215040 |- align=center BGCOLOR="#e0e0f0" !62 |<!-- [o3o3x3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_1,4,5{4,3⁶}||[[Bisteriruncinated 8-cube]]<BR>Bicelliprismated octeract||||||||||||||860160||143360 |- align=center BGCOLOR="#f0e0e0" !63 |<!-- [x3o3o3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,4,6{3⁶,4}||[[Hexistericated 8-orthoplex]]<BR>Peticellated diacosipentacontahexazetton||||||||||||||860160||107520 |- align=center BGCOLOR="#e0e0f0" !64 |<!-- [o3x3o3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_1,3,6{4,3⁶}||[[Bipenticantellated 8-cube]]<BR>Biterirhombated octeract||||||||||||||1720320||215040 |- align=center BGCOLOR="#e0e0f0" !65 |<!-- [o3o3x3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_1,3,5{4,3⁶}||[[Bistericantellated 8-cube]]<BR>Bicellirhombated octeract||||||||||||||1505280||215040 |- align=center BGCOLOR="#e0e0f0" !66 |<!-- [o3o3o3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_1,3,4{4,3⁶}||[[Biruncicantellated 8-cube]]<BR>Biprismatorhombated octeract||||||||||||||537600||107520 |- align=center BGCOLOR="#f0e0e0" !67 |<!-- [x3o3o3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,5,6{3⁶,4}||[[Hexipentellated 8-orthoplex]]<BR>Petiterated diacosipentacontahexazetton||||||||||||||258048||43008 |- align=center BGCOLOR="#e0e0f0" !68 |<!-- [o3x3o3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}}}||t_1,2,6{4,3⁶}||[[Bipentitruncated 8-cube]]<BR>Biteritruncated octeract||||||||||||||752640||107520 |- align=center BGCOLOR="#e0e0f0" !69 |<!-- [o3o3x3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}}}||t_1,2,5{4,3⁶}||[[Bisteritruncated 8-cube]]<BR>Bicellitruncated octeract||||||||||||||1003520||143360 |- align=center BGCOLOR="#e0e0f0" !70 |<!-- [o3o3o3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}}}||t_1,2,4{4,3⁶}||[[Biruncitruncated 8-cube]]<BR>Biprismatotruncated octeract||||||||||||||645120||107520 |- align=center BGCOLOR="#e0e0f0" !71 |<!-- [o3o3o3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}}}||t_1,2,3{4,3⁶}||[[Bicantitruncated 8-cube]]<BR>Great birhombated octeract||||||||||||||172032||43008 |- align=center BGCOLOR="#f0e0e0" !72 |<!-- [x3x3o3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,7{3⁶,4}||[[Heptitruncated 8-orthoplex]]<BR>Exitruncated diacosipentacontahexazetton||||||||||||||93184||14336 |- align=center BGCOLOR="#f0e0e0" !73 |<!-- [x3o3x3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,7{3⁶,4}||[[Hepticantellated 8-orthoplex]]<BR>Exirhombated diacosipentacontahexazetton||||||||||||||365568||43008 |- align=center BGCOLOR="#e0e0f0" !74 |<!-- [o3x3x3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_0,5,6{4,3⁶}||[[Hexipentellated 8-cube]]<BR>Petiterated octeract||||||||||||||258048||43008 |- align=center BGCOLOR="#f0e0e0" !75 |<!-- [x3o3o3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,7{3⁶,4}||[[Heptiruncinated 8-orthoplex]]<BR>Exiprismated diacosipentacontahexazetton||||||||||||||680960||71680 |- align=center BGCOLOR="#e0e0f0" !76 |<!-- [o3x3o3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_0,4,6{4,3⁶}||[[Hexistericated 8-cube]]<BR>Peticellated octeract||||||||||||||860160||107520 |- align=center BGCOLOR="#e0e0f0" !77 |<!-- [o3o3x3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_0,4,5{4,3⁶}||[[Pentistericated 8-cube]]<BR>Tericellated octeract||||||||||||||394240||71680 |- align=center BGCOLOR="#e0e0f0" !78 |<!-- [x3o3o3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,3,7{4,3⁶}||[[Heptiruncinated 8-cube]]<BR>Exiprismated octeract||||||||||||||680960||71680 |- align=center BGCOLOR="#e0e0f0" !79 |<!-- [o3x3o3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_0,3,6{4,3⁶}||[[Hexiruncinated 8-cube]]<BR>Petiprismated octeract||||||||||||||1290240||143360 |- align=center BGCOLOR="#e0e0f0" !80 |<!-- [o3o3x3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_0,3,5{4,3⁶}||[[Pentiruncinated 8-cube]]<BR>Teriprismated octeract||||||||||||||1075200||143360 |- align=center BGCOLOR="#e0e0f0" !81 |<!-- [o3o3o3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_0,3,4{4,3⁶}||[[Steriruncinated 8-cube]]<BR>Celliprismated octeract||||||||||||||358400||71680 |- align=center BGCOLOR="#e0e0f0" !82 |<!-- [x3o3o3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,2,7{4,3⁶}||[[Hepticantellated 8-cube]]<BR>Exirhombated octeract||||||||||||||365568||43008 |- align=center BGCOLOR="#e0e0f0" !83 |<!-- [o3x3o3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}}}||t_0,2,6{4,3⁶}||[[Hexicantellated 8-cube]]<BR>Petirhombated octeract||||||||||||||967680||107520 |- align=center BGCOLOR="#e0e0f0" !84 |<!-- [o3o3x3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}}}||t_0,2,5{4,3⁶}||[[Penticantellated 8-cube]]<BR>Terirhombated octeract||||||||||||||1218560||143360 |- align=center BGCOLOR="#e0e0f0" !85 |<!-- [o3o3o3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}}}||t_0,2,4{4,3⁶}||[[Stericantellated 8-cube]]<BR>Cellirhombated octeract||||||||||||||752640||107520 |- align=center BGCOLOR="#e0e0f0" !86 |<!-- [o3o3o3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}}}||t_0,2,3{4,3⁶}||[[Runcicantellated 8-cube]]<BR>Prismatorhombated octeract||||||||||||||193536||43008 |- align=center BGCOLOR="#e0e0f0" !87 |<!-- [x3o3o3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,1,7{4,3⁶}||[[Heptitruncated 8-cube]]<BR>Exitruncated octeract||||||||||||||93184||14336 |- align=center BGCOLOR="#e0e0f0" !88 |<!-- [o3x3o3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}}}||t_0,1,6{4,3⁶}||[[Hexitruncated 8-cube]]<BR>Petitruncated octeract||||||||||||||344064||43008 |- align=center BGCOLOR="#e0e0f0" !89 |<!-- [o3o3x3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}}}||t_0,1,5{4,3⁶}||[[Pentitruncated 8-cube]]<BR>Teritruncated octeract||||||||||||||609280||71680 |- align=center BGCOLOR="#e0e0f0" !90 |<!-- [o3o3o3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}}}||t_0,1,4{4,3⁶}||[[Steritruncated 8-cube]]<BR>Cellitruncated octeract||||||||||||||573440||71680 |- align=center BGCOLOR="#e0e0f0" !91 |<!-- [o3o3o3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}}}||t_0,1,3{4,3⁶}||[[Runcitruncated 8-cube]]<BR>Prismatotruncated octeract||||||||||||||279552||43008 |- align=center BGCOLOR="#e0e0f0" !92 |<!-- [o3o3o3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}}}||t_0,1,2{4,3⁶}||[[Cantitruncated 8-cube]]<BR>Great rhombated octeract||||||||||||||57344||14336 |- align=center BGCOLOR="#f0e0e0" !93 |<!-- [x3x3x3x3o3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3{3⁶,4}||[[Runcicantitruncated 8-orthoplex]]<BR>Great prismated diacosipentacontahexazetton||||||||||||||147840||26880 |- align=center BGCOLOR="#f0e0e0" !94 |<!-- [x3x3x3o3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4{3⁶,4}||[[Stericantitruncated 8-orthoplex]]<BR>Celligreatorhombated diacosipentacontahexazetton||||||||||||||860160||107520 |- align=center BGCOLOR="#f0e0e0" !95 |<!-- [x3x3o3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4{3⁶,4}||[[Steriruncitruncated 8-orthoplex]]<BR>Celliprismatotruncated diacosipentacontahexazetton||||||||||||||591360||107520 |- align=center BGCOLOR="#f0e0e0" !96 |<!-- [x3o3x3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4{3⁶,4}||[[Steriruncicantellated 8-orthoplex]]<BR>Celliprismatorhombated diacosipentacontahexazetton||||||||||||||591360||107520 |- align=center BGCOLOR="#f0e0e0" !97 |<!-- [o3x3x3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,4{3⁶,4}||[[Biruncicantitruncated 8-orthoplex]]<BR>Great biprismated diacosipentacontahexazetton||||||||||||||537600||107520 |- align=center BGCOLOR="#f0e0e0" !98 |<!-- [x3x3x3o3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,5{3⁶,4}||[[Penticantitruncated 8-orthoplex]]<BR>Terigreatorhombated diacosipentacontahexazetton||||||||||||||1827840||215040 |- align=center BGCOLOR="#f0e0e0" !99 |<!-- [x3x3o3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,5{3⁶,4}||[[Pentiruncitruncated 8-orthoplex]]<BR>Teriprismatotruncated diacosipentacontahexazetton||||||||||||||2419200||322560 |- align=center BGCOLOR="#f0e0e0" !100 |<!-- [x3o3x3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,5{3⁶,4}||[[Pentiruncicantellated 8-orthoplex]]<BR>Teriprismatorhombated diacosipentacontahexazetton||||||||||||||2257920||322560 |- align=center BGCOLOR="#f0e0e0" !101 |<!-- [o3x3x3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,5{3⁶,4}||[[Bistericantitruncated 8-orthoplex]]<BR>Bicelligreatorhombated diacosipentacontahexazetton||||||||||||||2096640||322560 |- align=center BGCOLOR="#f0e0e0" !102 |<!-- [x3x3o3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4,5{3⁶,4}||[[Pentisteritruncated 8-orthoplex]]<BR>Tericellitruncated diacosipentacontahexazetton||||||||||||||1182720||215040 |- align=center BGCOLOR="#f0e0e0" !103 |<!-- [x3o3x3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,4,5{3⁶,4}||[[Pentistericantellated 8-orthoplex]]<BR>Tericellirhombated diacosipentacontahexazetton||||||||||||||1935360||322560 |- align=center BGCOLOR="#f0e0e0" !104 |<!-- [o3x3x3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,4,5{3⁶,4}||[[Bisteriruncitruncated 8-orthoplex]]<BR>Bicelliprismatotruncated diacosipentacontahexazetton||||||||||||||1612800||322560 |- align=center BGCOLOR="#f0e0e0" !105 |<!-- [x3o3o3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,4,5{3⁶,4}||[[Pentisteriruncinated 8-orthoplex]]<BR>Tericelliprismated diacosipentacontahexazetton||||||||||||||1182720||215040 |- align=center BGCOLOR="#f0e0e0" !106 |<!-- [o3x3o3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3,4,5{3⁶,4}||[[Bisteriruncicantellated 8-orthoplex]]<BR>Bicelliprismatorhombated diacosipentacontahexazetton||||||||||||||1774080||322560 |- align=center BGCOLOR="#e0f0e0" !107 |<!-- [o3o3x3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_2,3,4,5{4,3⁶}||[[Triruncicantitruncated 8-cube]]<BR>Great triprismato-octeractidiacosipentacontahexazetton||||||||||||||967680||215040 |- align=center BGCOLOR="#f0e0e0" !108 |<!-- [x3x3x3o3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,6{3⁶,4}||[[Hexicantitruncated 8-orthoplex]]<BR>Petigreatorhombated diacosipentacontahexazetton||||||||||||||1505280||215040 |- align=center BGCOLOR="#f0e0e0" !109 |<!-- [x3x3o3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,6{3⁶,4}||[[Hexiruncitruncated 8-orthoplex]]<BR>Petiprismatotruncated diacosipentacontahexazetton||||||||||||||3225600||430080 |- align=center BGCOLOR="#f0e0e0" !110 |<!-- [x3o3x3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,6{3⁶,4}||[[Hexiruncicantellated 8-orthoplex]]<BR>Petiprismatorhombated diacosipentacontahexazetton||||||||||||||2795520||430080 |- align=center BGCOLOR="#f0e0e0" !111 |<!-- [o3x3x3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,6{3⁶,4}||[[Bipenticantitruncated 8-orthoplex]]<BR>Biterigreatorhombated diacosipentacontahexazetton||||||||||||||2580480||430080 |- align=center BGCOLOR="#f0e0e0" !112 |<!-- [x3x3o3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4,6{3⁶,4}||[[Hexisteritruncated 8-orthoplex]]<BR>Peticellitruncated diacosipentacontahexazetton||||||||||||||3010560||430080 |- align=center BGCOLOR="#f0e0e0" !113 |<!-- [x3o3x3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,4,6{3⁶,4}||[[Hexistericantellated 8-orthoplex]]<BR>Peticellirhombated diacosipentacontahexazetton||||||||||||||4515840||645120 |- align=center BGCOLOR="#f0e0e0" !114 |<!-- [o3x3x3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,4,6{3⁶,4}||[[Bipentiruncitruncated 8-orthoplex]]<BR>Biteriprismatotruncated diacosipentacontahexazetton||||||||||||||3870720||645120 |- align=center BGCOLOR="#f0e0e0" !115 |<!-- [x3o3o3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,4,6{3⁶,4}||[[Hexisteriruncinated 8-orthoplex]]<BR>Peticelliprismated diacosipentacontahexazetton||||||||||||||2580480||430080 |- align=center BGCOLOR="#e0f0e0" !116 |<!-- [o3x3o3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_1,3,4,6{4,3⁶}||[[Bipentiruncicantellated 8-cube]]<BR>Biteriprismatorhombi-octeractidiacosipentacontahexazetton||||||||||||||3870720||645120 |- align=center BGCOLOR="#e0e0f0" !117 |<!-- [o3o3x3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_1,3,4,5{4,3⁶}||[[Bisteriruncicantellated 8-cube]]<BR>Bicelliprismatorhombated octeract||||||||||||||2150400||430080 |- align=center BGCOLOR="#f0e0e0" !118 |<!-- [x3x3o3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,5,6{3⁶,4}||[[Hexipentitruncated 8-orthoplex]]<BR>Petiteritruncated diacosipentacontahexazetton||||||||||||||1182720||215040 |- align=center BGCOLOR="#f0e0e0" !119 |<!-- [x3o3x3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,5,6{3⁶,4}||[[Hexipenticantellated 8-orthoplex]]<BR>Petiterirhombated diacosipentacontahexazetton||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0f0e0" !120 |<!-- [o3x3x3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,5,6{4,3⁶}||[[Bipentisteritruncated 8-cube]]<BR>Bitericellitrunki-octeractidiacosipentacontahexazetton||||||||||||||2150400||430080 |- align=center BGCOLOR="#f0e0e0" !121 |<!-- [x3o3o3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,5,6{3⁶,4}||[[Hexipentiruncinated 8-orthoplex]]<BR>Petiteriprismated diacosipentacontahexazetton||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0e0f0" !122 |<!-- [o3x3o3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_1,2,4,6{4,3⁶}||[[Bipentiruncitruncated 8-cube]]<BR>Biteriprismatotruncated octeract||||||||||||||3870720||645120 |- align=center BGCOLOR="#e0e0f0" !123 |<!-- [o3o3x3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_1,2,4,5{4,3⁶}||[[Bisteriruncitruncated 8-cube]]<BR>Bicelliprismatotruncated octeract||||||||||||||1935360||430080 |- align=center BGCOLOR="#f0e0e0" !124 |<!-- [x3o3o3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,4,5,6{3⁶,4}||[[Hexipentistericated 8-orthoplex]]<BR>Petitericellated diacosipentacontahexazetton||||||||||||||1182720||215040 |- align=center BGCOLOR="#e0e0f0" !125 |<!-- [o3x3o3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_1,2,3,6{4,3⁶}||[[Bipenticantitruncated 8-cube]]<BR>Biterigreatorhombated octeract||||||||||||||2580480||430080 |- align=center BGCOLOR="#e0e0f0" !126 |<!-- [o3o3x3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_1,2,3,5{4,3⁶}||[[Bistericantitruncated 8-cube]]<BR>Bicelligreatorhombated octeract||||||||||||||2365440||430080 |- align=center BGCOLOR="#e0e0f0" !127 |<!-- [o3o3o3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_1,2,3,4{4,3⁶}||[[Biruncicantitruncated 8-cube]]<BR>Great biprismated octeract||||||||||||||860160||215040 |- align=center BGCOLOR="#f0e0e0" !128 |<!-- [x3x3x3o3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,7{3⁶,4}||[[Hepticantitruncated 8-orthoplex]]<BR>Exigreatorhombated diacosipentacontahexazetton||||||||||||||516096||86016 |- align=center BGCOLOR="#f0e0e0" !129 |<!-- [x3x3o3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,7{3⁶,4}||[[Heptiruncitruncated 8-orthoplex]]<BR>Exiprismatotruncated diacosipentacontahexazetton||||||||||||||1612800||215040 |- align=center BGCOLOR="#f0e0e0" !130 |<!-- [x3o3x3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,7{3⁶,4}||[[Heptiruncicantellated 8-orthoplex]]<BR>Exiprismatorhombated diacosipentacontahexazetton||||||||||||||1290240||215040 |- align=center BGCOLOR="#e0e0f0" !131 |<!-- [o3x3x3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,4,5,6{4,3⁶}||[[Hexipentistericated 8-cube]]<BR>Petitericellated octeract||||||||||||||1182720||215040 |- align=center BGCOLOR="#f0e0e0" !132 |<!-- [x3x3o3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4,7{3⁶,4}||[[Heptisteritruncated 8-orthoplex]]<BR>Exicellitruncated diacosipentacontahexazetton||||||||||||||2293760||286720 |- align=center BGCOLOR="#f0e0e0" !133 |<!-- [x3o3x3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,4,7{3⁶,4}||[[Heptistericantellated 8-orthoplex]]<BR>Exicellirhombated diacosipentacontahexazetton||||||||||||||3225600||430080 |- align=center BGCOLOR="#e0e0f0" !134 |<!-- [o3x3x3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_0,3,5,6{4,3⁶}||[[Hexipentiruncinated 8-cube]]<BR>Petiteriprismated octeract||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0f0e0" !135 |<!-- [x3o3o3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,4,7{4,3⁶}||[[Heptisteriruncinated 8-cube]]<BR>Exicelliprismato-octeractidiacosipentacontahexazetton||||||||||||||1720320||286720 |- align=center BGCOLOR="#e0e0f0" !136 |<!-- [o3x3o3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_0,3,4,6{4,3⁶}||[[Hexisteriruncinated 8-cube]]<BR>Peticelliprismated octeract||||||||||||||2580480||430080 |- align=center BGCOLOR="#e0e0f0" !137 |<!-- [o3o3x3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_0,3,4,5{4,3⁶}||[[Pentisteriruncinated 8-cube]]<BR>Tericelliprismated octeract||||||||||||||1433600||286720 |- align=center BGCOLOR="#f0e0e0" !138 |<!-- [x3x3o3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,5,7{3⁶,4}||[[Heptipentitruncated 8-orthoplex]]<BR>Exiteritruncated diacosipentacontahexazetton||||||||||||||1612800||215040 |- align=center BGCOLOR="#e0f0e0" !139 |<!-- [x3o3x3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,5,7{4,3⁶}||[[Heptipenticantellated 8-cube]]<BR>Exiterirhombi-octeractidiacosipentacontahexazetton||||||||||||||3440640||430080 |- align=center BGCOLOR="#e0e0f0" !140 |<!-- [o3x3x3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_0,2,5,6{4,3⁶}||[[Hexipenticantellated 8-cube]]<BR>Petiterirhombated octeract||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0e0f0" !141 |<!-- [x3o3o3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,2,4,7{4,3⁶}||[[Heptistericantellated 8-cube]]<BR>Exicellirhombated octeract||||||||||||||3225600||430080 |- align=center BGCOLOR="#e0e0f0" !142 |<!-- [o3x3o3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_0,2,4,6{4,3⁶}||[[Hexistericantellated 8-cube]]<BR>Peticellirhombated octeract||||||||||||||4515840||645120 |- align=center BGCOLOR="#e0e0f0" !143 |<!-- [o3o3x3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_0,2,4,5{4,3⁶}||[[Pentistericantellated 8-cube]]<BR>Tericellirhombated octeract||||||||||||||2365440||430080 |- align=center BGCOLOR="#e0e0f0" !144 |<!-- [x3o3o3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,2,3,7{4,3⁶}||[[Heptiruncicantellated 8-cube]]<BR>Exiprismatorhombated octeract||||||||||||||1290240||215040 |- align=center BGCOLOR="#e0e0f0" !145 |<!-- [o3x3o3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_0,2,3,6{4,3⁶}||[[Hexiruncicantellated 8-cube]]<BR>Petiprismatorhombated octeract||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0e0f0" !146 |<!-- [o3o3x3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_0,2,3,5{4,3⁶}||[[Pentiruncicantellated 8-cube]]<BR>Teriprismatorhombated octeract||||||||||||||2580480||430080 |- align=center BGCOLOR="#e0e0f0" !147 |<!-- [o3o3o3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_0,2,3,4{4,3⁶}||[[Steriruncicantellated 8-cube]]<BR>Celliprismatorhombated octeract||||||||||||||967680||215040 |- align=center BGCOLOR="#e0f0e0" !148 |<!-- [x3x3o3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,6,7{4,3⁶}||[[Heptihexitruncated 8-cube]]<BR>Exipetitrunki-octeractidiacosipentacontahexazetton||||||||||||||516096||86016 |- align=center BGCOLOR="#e0e0f0" !149 |<!-- [x3o3x3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,1,5,7{4,3⁶}||[[Heptipentitruncated 8-cube]]<BR>Exiteritruncated octeract||||||||||||||1612800||215040 |- align=center BGCOLOR="#e0e0f0" !150 |<!-- [o3x3x3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_0,1,5,6{4,3⁶}||[[Hexipentitruncated 8-cube]]<BR>Petiteritruncated octeract||||||||||||||1182720||215040 |- align=center BGCOLOR="#e0e0f0" !151 |<!-- [x3o3o3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,1,4,7{4,3⁶}||[[Heptisteritruncated 8-cube]]<BR>Exicellitruncated octeract||||||||||||||2293760||286720 |- align=center BGCOLOR="#e0e0f0" !152 |<!-- [o3x3o3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_0,1,4,6{4,3⁶}||[[Hexisteritruncated 8-cube]]<BR>Peticellitruncated octeract||||||||||||||3010560||430080 |- align=center BGCOLOR="#e0e0f0" !153 |<!-- [o3o3x3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_0,1,4,5{4,3⁶}||[[Pentisteritruncated 8-cube]]<BR>Tericellitruncated octeract||||||||||||||1433600||286720 |- align=center BGCOLOR="#e0e0f0" !154 |<!-- [x3o3o3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,1,3,7{4,3⁶}||[[Heptiruncitruncated 8-cube]]<BR>Exiprismatotruncated octeract||||||||||||||1612800||215040 |- align=center BGCOLOR="#e0e0f0" !155 |<!-- [o3x3o3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_0,1,3,6{4,3⁶}||[[Hexiruncitruncated 8-cube]]<BR>Petiprismatotruncated octeract||||||||||||||3225600||430080 |- align=center BGCOLOR="#e0e0f0" !156 |<!-- [o3o3x3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_0,1,3,5{4,3⁶}||[[Pentiruncitruncated 8-cube]]<BR>Teriprismatotruncated octeract||||||||||||||2795520||430080 |- align=center BGCOLOR="#e0e0f0" !157 |<!-- [o3o3o3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_0,1,3,4{4,3⁶}||[[Steriruncitruncated 8-cube]]<BR>Celliprismatotruncated octeract||||||||||||||967680||215040 |- align=center BGCOLOR="#e0e0f0" !158 |<!-- [x3o3o3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}}}||t_0,1,2,7{4,3⁶}||[[Hepticantitruncated 8-cube]]<BR>Exigreatorhombated octeract||||||||||||||516096||86016 |- align=center BGCOLOR="#e0e0f0" !159 |<!-- [o3x3o3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}}}||t_0,1,2,6{4,3⁶}||[[Hexicantitruncated 8-cube]]<BR>Petigreatorhombated octeract||||||||||||||1505280||215040 |- align=center BGCOLOR="#e0e0f0" !160 |<!-- [o3o3x3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}}}||t_0,1,2,5{4,3⁶}||[[Penticantitruncated 8-cube]]<BR>Terigreatorhombated octeract||||||||||||||2007040||286720 |- align=center BGCOLOR="#e0e0f0" !161 |<!-- [o3o3o3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}}}||t_0,1,2,4{4,3⁶}||[[Stericantitruncated 8-cube]]<BR>Celligreatorhombated octeract||||||||||||||1290240||215040 |- align=center BGCOLOR="#e0e0f0" !162 |<!-- [o3o3o3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}}}||t_0,1,2,3{4,3⁶}||[[Runcicantitruncated 8-cube]]<BR>Great prismated octeract||||||||||||||344064||86016 |- align=center BGCOLOR="#f0e0e0" !163 |<!-- [x3x3x3x3x3o3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,4{3⁶,4}||[[Steriruncicantitruncated 8-orthoplex]]<BR>Great cellated diacosipentacontahexazetton||||||||||||||1075200||215040 |- align=center BGCOLOR="#f0e0e0" !164 |<!-- [x3x3x3x3o3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,5{3⁶,4}||[[Pentiruncicantitruncated 8-orthoplex]]<BR>Terigreatoprismated diacosipentacontahexazetton||||||||||||||4193280||645120 |- align=center BGCOLOR="#f0e0e0" !165 |<!-- [x3x3x3o3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,5{3⁶,4}||[[Pentistericantitruncated 8-orthoplex]]<BR>Tericelligreatorhombated diacosipentacontahexazetton||||||||||||||3225600||645120 |- align=center BGCOLOR="#f0e0e0" !166 |<!-- [x3x3o3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,5{3⁶,4}||[[Pentisteriruncitruncated 8-orthoplex]]<BR>Tericelliprismatotruncated diacosipentacontahexazetton||||||||||||||3225600||645120 |- align=center BGCOLOR="#f0e0e0" !167 |<!-- [x3o3x3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4,5{3⁶,4}||[[Pentisteriruncicantellated 8-orthoplex]]<BR>Tericelliprismatorhombated diacosipentacontahexazetton||||||||||||||3225600||645120 |- align=center BGCOLOR="#f0e0e0" !168 |<!-- [o3x3x3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,4,5{3⁶,4}||[[Bisteriruncicantitruncated 8-orthoplex]]<BR>Great bicellated diacosipentacontahexazetton||||||||||||||2903040||645120 |- align=center BGCOLOR="#f0e0e0" !169 |<!-- [x3x3x3x3o3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,6{3⁶,4}||[[Hexiruncicantitruncated 8-orthoplex]]<BR>Petigreatoprismated diacosipentacontahexazetton||||||||||||||5160960||860160 |- align=center BGCOLOR="#f0e0e0" !170 |<!-- [x3x3x3o3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,6{3⁶,4}||[[Hexistericantitruncated 8-orthoplex]]<BR>Peticelligreatorhombated diacosipentacontahexazetton||||||||||||||7741440||1290240 |- align=center BGCOLOR="#f0e0e0" !171 |<!-- [x3x3o3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,6{3⁶,4}||[[Hexisteriruncitruncated 8-orthoplex]]<BR>Peticelliprismatotruncated diacosipentacontahexazetton||||||||||||||7096320||1290240 |- align=center BGCOLOR="#f0e0e0" !172 |<!-- [x3o3x3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4,6{3⁶,4}||[[Hexisteriruncicantellated 8-orthoplex]]<BR>Peticelliprismatorhombated diacosipentacontahexazetton||||||||||||||7096320||1290240 |- align=center BGCOLOR="#f0e0e0" !173 |<!-- [o3x3x3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,4,6{3⁶,4}||[[Bipentiruncicantitruncated 8-orthoplex]]<BR>Biterigreatoprismated diacosipentacontahexazetton||||||||||||||6451200||1290240 |- align=center BGCOLOR="#f0e0e0" !174 |<!-- [x3x3x3o3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,5,6{3⁶,4}||[[Hexipenticantitruncated 8-orthoplex]]<BR>Petiterigreatorhombated diacosipentacontahexazetton||||||||||||||4300800||860160 |- align=center BGCOLOR="#f0e0e0" !175 |<!-- [x3x3o3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,5,6{3⁶,4}||[[Hexipentiruncitruncated 8-orthoplex]]<BR>Petiteriprismatotruncated diacosipentacontahexazetton||||||||||||||7096320||1290240 |- align=center BGCOLOR="#f0e0e0" !176 |<!-- [x3o3x3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,5,6{3⁶,4}||[[Hexipentiruncicantellated 8-orthoplex]]<BR>Petiteriprismatorhombated diacosipentacontahexazetton||||||||||||||6451200||1290240 |- align=center BGCOLOR="#f0e0e0" !177 |<!-- [o3x3x3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,5,6{3⁶,4}||[[Bipentistericantitruncated 8-orthoplex]]<BR>Bitericelligreatorhombated diacosipentacontahexazetton||||||||||||||5806080||1290240 |- align=center BGCOLOR="#f0e0e0" !178 |<!-- [x3x3o3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4,5,6{3⁶,4}||[[Hexipentisteritruncated 8-orthoplex]]<BR>Petitericellitruncated diacosipentacontahexazetton||||||||||||||4300800||860160 |- align=center BGCOLOR="#f0e0e0" !179 |<!-- [x3o3x3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,4,5,6{3⁶,4}||[[Hexipentistericantellated 8-orthoplex]]<BR>Petitericellirhombated diacosipentacontahexazetton||||||||||||||7096320||1290240 |- align=center BGCOLOR="#e0e0f0" !180 |<!-- [o3x3x3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_1,2,3,5,6{4,3⁶}||[[Bipentistericantitruncated 8-cube]]<BR>Bitericelligreatorhombated octeract||||||||||||||5806080||1290240 |- align=center BGCOLOR="#f0e0e0" !181 |<!-- [x3o3o3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,3,4,5,6{3⁶,4}||[[Hexipentisteriruncinated 8-orthoplex]]<BR>Petitericelliprismated diacosipentacontahexazetton||||||||||||||4300800||860160 |- align=center BGCOLOR="#e0e0f0" !182 |<!-- [o3x3o3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_1,2,3,4,6{4,3⁶}||[[Bipentiruncicantitruncated 8-cube]]<BR>Biterigreatoprismated octeract||||||||||||||6451200||1290240 |- align=center BGCOLOR="#e0e0f0" !183 |<!-- [o3o3x3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_1,2,3,4,5{4,3⁶}||[[Bisteriruncicantitruncated 8-cube]]<BR>Great bicellated octeract||||||||||||||3440640||860160 |- align=center BGCOLOR="#f0e0e0" !184 |<!-- [x3x3x3x3o3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,7{3⁶,4}||[[Heptiruncicantitruncated 8-orthoplex]]<BR>Exigreatoprismated diacosipentacontahexazetton||||||||||||||2365440||430080 |- align=center BGCOLOR="#f0e0e0" !185 |<!-- [x3x3x3o3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,7{3⁶,4}||[[Heptistericantitruncated 8-orthoplex]]<BR>Exicelligreatorhombated diacosipentacontahexazetton||||||||||||||5591040||860160 |- align=center BGCOLOR="#f0e0e0" !186 |<!-- [x3x3o3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,7{3⁶,4}||[[Heptisteriruncitruncated 8-orthoplex]]<BR>Exicelliprismatotruncated diacosipentacontahexazetton||||||||||||||4730880||860160 |- align=center BGCOLOR="#f0e0e0" !187 |<!-- [x3o3x3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4,7{3⁶,4}||[[Heptisteriruncicantellated 8-orthoplex]]<BR>Exicelliprismatorhombated diacosipentacontahexazetton||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !188 |<!-- [o3x3x3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,3,4,5,6{4,3⁶}||[[Hexipentisteriruncinated 8-cube]]<BR>Petitericelliprismated octeract||||||||||||||4300800||860160 |- align=center BGCOLOR="#f0e0e0" !189 |<!-- [x3x3x3o3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,5,7{3⁶,4}||[[Heptipenticantitruncated 8-orthoplex]]<BR>Exiterigreatorhombated diacosipentacontahexazetton||||||||||||||5591040||860160 |- align=center BGCOLOR="#f0e0e0" !190 |<!-- [x3x3o3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,5,7{3⁶,4}||[[Heptipentiruncitruncated 8-orthoplex]]<BR>Exiteriprismatotruncated diacosipentacontahexazetton||||||||||||||8386560||1290240 |- align=center BGCOLOR="#f0e0e0" !191 |<!-- [x3o3x3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,5,7{3⁶,4}||[[Heptipentiruncicantellated 8-orthoplex]]<BR>Exiteriprismatorhombated diacosipentacontahexazetton||||||||||||||7741440||1290240 |- align=center BGCOLOR="#e0e0f0" !192 |<!-- [o3x3x3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,2,4,5,6{4,3⁶}||[[Hexipentistericantellated 8-cube]]<BR>Petitericellirhombated octeract||||||||||||||7096320||1290240 |- align=center BGCOLOR="#f0e0e0" !193 |<!-- [x3x3o3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,4,5,7{3⁶,4}||[[Heptipentisteritruncated 8-orthoplex]]<BR>Exitericellitruncated diacosipentacontahexazetton||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !194 |<!-- [x3o3x3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,2,3,5,7{4,3⁶}||[[Heptipentiruncicantellated 8-cube]]<BR>Exiteriprismatorhombated octeract||||||||||||||7741440||1290240 |- align=center BGCOLOR="#e0e0f0" !195 |<!-- [o3x3x3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_0,2,3,5,6{4,3⁶}||[[Hexipentiruncicantellated 8-cube]]<BR>Petiteriprismatorhombated octeract||||||||||||||6451200||1290240 |- align=center BGCOLOR="#e0e0f0" !196 |<!-- [x3o3o3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,2,3,4,7{4,3⁶}||[[Heptisteriruncicantellated 8-cube]]<BR>Exicelliprismatorhombated octeract||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !197 |<!-- [o3x3o3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_0,2,3,4,6{4,3⁶}||[[Hexisteriruncicantellated 8-cube]]<BR>Peticelliprismatorhombated octeract||||||||||||||7096320||1290240 |- align=center BGCOLOR="#e0e0f0" !198 |<!-- [o3o3x3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_0,2,3,4,5{4,3⁶}||[[Pentisteriruncicantellated 8-cube]]<BR>Tericelliprismatorhombated octeract||||||||||||||3870720||860160 |- align=center BGCOLOR="#f0e0e0" !199 |<!-- [x3x3x3o3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,6,7{3⁶,4}||[[Heptihexicantitruncated 8-orthoplex]]<BR>Exipetigreatorhombated diacosipentacontahexazetton||||||||||||||2365440||430080 |- align=center BGCOLOR="#f0e0e0" !200 |<!-- [x3x3o3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,6,7{3⁶,4}||[[Heptihexiruncitruncated 8-orthoplex]]<BR>Exipetiprismatotruncated diacosipentacontahexazetton||||||||||||||5591040||860160 |- align=center BGCOLOR="#e0e0f0" !201 |<!-- [x3o3x3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,1,4,5,7{4,3⁶}||[[Heptipentisteritruncated 8-cube]]<BR>Exitericellitruncated octeract||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !202 |<!-- [o3x3x3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,1,4,5,6{4,3⁶}||[[Hexipentisteritruncated 8-cube]]<BR>Petitericellitruncated octeract||||||||||||||4300800||860160 |- align=center BGCOLOR="#e0e0f0" !203 |<!-- [x3x3o3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,3,6,7{4,3⁶}||[[Heptihexiruncitruncated 8-cube]]<BR>Exipetiprismatotruncated octeract||||||||||||||5591040||860160 |- align=center BGCOLOR="#e0e0f0" !204 |<!-- [x3o3x3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,1,3,5,7{4,3⁶}||[[Heptipentiruncitruncated 8-cube]]<BR>Exiteriprismatotruncated octeract||||||||||||||8386560||1290240 |- align=center BGCOLOR="#e0e0f0" !205 |<!-- [o3x3x3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_0,1,3,5,6{4,3⁶}||[[Hexipentiruncitruncated 8-cube]]<BR>Petiteriprismatotruncated octeract||||||||||||||7096320||1290240 |- align=center BGCOLOR="#e0e0f0" !206 |<!-- [x3o3o3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,1,3,4,7{4,3⁶}||[[Heptisteriruncitruncated 8-cube]]<BR>Exicelliprismatotruncated octeract||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !207 |<!-- [o3x3o3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_0,1,3,4,6{4,3⁶}||[[Hexisteriruncitruncated 8-cube]]<BR>Peticelliprismatotruncated octeract||||||||||||||7096320||1290240 |- align=center BGCOLOR="#e0e0f0" !208 |<!-- [o3o3x3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_0,1,3,4,5{4,3⁶}||[[Pentisteriruncitruncated 8-cube]]<BR>Tericelliprismatotruncated octeract||||||||||||||3870720||860160 |- align=center BGCOLOR="#e0e0f0" !209 |<!-- [x3x3o3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,2,6,7{4,3⁶}||[[Heptihexicantitruncated 8-cube]]<BR>Exipetigreatorhombated octeract||||||||||||||2365440||430080 |- align=center BGCOLOR="#e0e0f0" !210 |<!-- [x3o3x3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}}}||t_0,1,2,5,7{4,3⁶}||[[Heptipenticantitruncated 8-cube]]<BR>Exiterigreatorhombated octeract||||||||||||||5591040||860160 |- align=center BGCOLOR="#e0e0f0" !211 |<!-- [o3x3x3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}}}||t_0,1,2,5,6{4,3⁶}||[[Hexipenticantitruncated 8-cube]]<BR>Petiterigreatorhombated octeract||||||||||||||4300800||860160 |- align=center BGCOLOR="#e0e0f0" !212 |<!-- [x3o3o3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}}}||t_0,1,2,4,7{4,3⁶}||[[Heptistericantitruncated 8-cube]]<BR>Exicelligreatorhombated octeract||||||||||||||5591040||860160 |- align=center BGCOLOR="#e0e0f0" !213 |<!-- [o3x3o3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}}}||t_0,1,2,4,6{4,3⁶}||[[Hexistericantitruncated 8-cube]]<BR>Peticelligreatorhombated octeract||||||||||||||7741440||1290240 |- align=center BGCOLOR="#e0e0f0" !214 |<!-- [o3o3x3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}}}||t_0,1,2,4,5{4,3⁶}||[[Pentistericantitruncated 8-cube]]<BR>Tericelligreatorhombated octeract||||||||||||||3870720||860160 |- align=center BGCOLOR="#e0e0f0" !215 |<!-- [x3o3o3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}}}||t_0,1,2,3,7{4,3⁶}||[[Heptiruncicantitruncated 8-cube]]<BR>Exigreatoprismated octeract||||||||||||||2365440||430080 |- align=center BGCOLOR="#e0e0f0" !216 |<!-- [o3x3o3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}}}||t_0,1,2,3,6{4,3⁶}||[[Hexiruncicantitruncated 8-cube]]<BR>Petigreatoprismated octeract||||||||||||||5160960||860160 |- align=center BGCOLOR="#e0e0f0" !217 |<!-- [o3o3x3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}}}||t_0,1,2,3,5{4,3⁶}||[[Pentiruncicantitruncated 8-cube]]<BR>Terigreatoprismated octeract||||||||||||||4730880||860160 |- align=center BGCOLOR="#e0e0f0" !218 |<!-- [o3o3o3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}}}||t_0,1,2,3,4{4,3⁶}||[[Steriruncicantitruncated 8-cube]]<BR>Great cellated octeract||||||||||||||1720320||430080 |- align=center BGCOLOR="#f0e0e0" !219 |<!-- [x3x3x3x3x3x3o4o] -->{{dark mode invert|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,4,5{3⁶,4}||[[Pentisteriruncicantitruncated 8-orthoplex]]<BR>Great terated diacosipentacontahexazetton||||||||||||||5806080||1290240 |- align=center BGCOLOR="#f0e0e0" !220 |<!-- [x3x3x3x3x3o3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,4,6{3⁶,4}||[[Hexisteriruncicantitruncated 8-orthoplex]]<BR>Petigreatocellated diacosipentacontahexazetton||||||||||||||12902400||2580480 |- align=center BGCOLOR="#f0e0e0" !221 |<!-- [x3x3x3x3o3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,5,6{3⁶,4}||[[Hexipentiruncicantitruncated 8-orthoplex]]<BR>Petiterigreatoprismated diacosipentacontahexazetton||||||||||||||11612160||2580480 |- align=center BGCOLOR="#f0e0e0" !222 |<!-- [x3x3x3o3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,5,6{3⁶,4}||[[Hexipentistericantitruncated 8-orthoplex]]<BR>Petitericelligreatorhombated diacosipentacontahexazetton||||||||||||||11612160||2580480 |- align=center BGCOLOR="#f0e0e0" !223 |<!-- [x3x3o3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,5,6{3⁶,4}||[[Hexipentisteriruncitruncated 8-orthoplex]]<BR>Petitericelliprismatotruncated diacosipentacontahexazetton||||||||||||||11612160||2580480 |- align=center BGCOLOR="#f0e0e0" !224 |<!-- [x3o3x3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4,5,6{3⁶,4}||[[Hexipentisteriruncicantellated 8-orthoplex]]<BR>Petitericelliprismatorhombated diacosipentacontahexazetton||||||||||||||11612160||2580480 |- align=center BGCOLOR="#e0f0e0" !225 |<!-- [o3x3x3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_1,2,3,4,5,6{4,3⁶}||[[Bipentisteriruncicantitruncated 8-cube]]<BR>Great biteri-octeractidiacosipentacontahexazetton||||||||||||||10321920||2580480 |- align=center BGCOLOR="#f0e0e0" !226 |<!-- [x3x3x3x3x3o3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,4,7{3⁶,4}||[[Heptisteriruncicantitruncated 8-orthoplex]]<BR>Exigreatocellated diacosipentacontahexazetton||||||||||||||8601600||1720320 |- align=center BGCOLOR="#f0e0e0" !227 |<!-- [x3x3x3x3o3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,5,7{3⁶,4}||[[Heptipentiruncicantitruncated 8-orthoplex]]<BR>Exiterigreatoprismated diacosipentacontahexazetton||||||||||||||14192640||2580480 |- align=center BGCOLOR="#f0e0e0" !228 |<!-- [x3x3x3o3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,5,7{3⁶,4}||[[Heptipentistericantitruncated 8-orthoplex]]<BR>Exitericelligreatorhombated diacosipentacontahexazetton||||||||||||||12902400||2580480 |- align=center BGCOLOR="#f0e0e0" !229 |<!-- [x3x3o3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,5,7{3⁶,4}||[[Heptipentisteriruncitruncated 8-orthoplex]]<BR>Exitericelliprismatotruncated diacosipentacontahexazetton||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0f0e0" !230 |<!-- [x3o3x3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,2,3,4,5,7{4,3⁶}||[[Heptipentisteriruncicantellated 8-cube]]<BR>Exitericelliprismatorhombi-octeractidiacosipentacontahexazetton||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0e0f0" !231 |<!-- [o3x3x3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,2,3,4,5,6{4,3⁶}||[[Hexipentisteriruncicantellated 8-cube]]<BR>Petitericelliprismatorhombated octeract||||||||||||||11612160||2580480 |- align=center BGCOLOR="#f0e0e0" !232 |<!-- [x3x3x3x3o3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,3,6,7{3⁶,4}||[[Heptihexiruncicantitruncated 8-orthoplex]]<BR>Exipetigreatoprismated diacosipentacontahexazetton||||||||||||||8601600||1720320 |- align=center BGCOLOR="#f0e0e0" !233 |<!-- [x3x3x3o3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,4,6,7{3⁶,4}||[[Heptihexistericantitruncated 8-orthoplex]]<BR>Exipeticelligreatorhombated diacosipentacontahexazetton||||||||||||||14192640||2580480 |- align=center BGCOLOR="#e0f0e0" !234 |<!-- [x3x3o3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,3,4,6,7{4,3⁶}||[[Heptihexisteriruncitruncated 8-cube]]<BR>Exipeticelliprismatotrunki-octeractidiacosipentacontahexazetton||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0e0f0" !235 |<!-- [x3o3x3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,1,3,4,5,7{4,3⁶}||[[Heptipentisteriruncitruncated 8-cube]]<BR>Exitericelliprismatotruncated octeract||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0e0f0" !236 |<!-- [o3x3x3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,1,3,4,5,6{4,3⁶}||[[Hexipentisteriruncitruncated 8-cube]]<BR>Petitericelliprismatotruncated octeract||||||||||||||11612160||2580480 |- align=center BGCOLOR="#e0f0e0" !237 |<!-- [x3x3x3o3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}}}||t_0,1,2,5,6,7{4,3⁶}||[[Heptihexipenticantitruncated 8-cube]]<BR>Exipetiterigreatorhombi-octeractidiacosipentacontahexazetton||||||||||||||8601600||1720320 |- align=center BGCOLOR="#e0e0f0" !238 |<!-- [x3x3o3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}}}||t_0,1,2,4,6,7{4,3⁶}||[[Heptihexistericantitruncated 8-cube]]<BR>Exipeticelligreatorhombated octeract||||||||||||||14192640||2580480 |- align=center BGCOLOR="#e0e0f0" !239 |<!-- [x3o3x3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}}}||t_0,1,2,4,5,7{4,3⁶}||[[Heptipentistericantitruncated 8-cube]]<BR>Exitericelligreatorhombated octeract||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0e0f0" !240 |<!-- [o3x3x3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}}}||t_0,1,2,4,5,6{4,3⁶}||[[Hexipentistericantitruncated 8-cube]]<BR>Petitericelligreatorhombated octeract||||||||||||||11612160||2580480 |- align=center BGCOLOR="#e0e0f0" !241 |<!-- [x3x3o3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}}}||t_0,1,2,3,6,7{4,3⁶}||[[Heptihexiruncicantitruncated 8-cube]]<BR>Exipetigreatoprismated octeract||||||||||||||8601600||1720320 |- align=center BGCOLOR="#e0e0f0" !242 |<!-- [x3o3x3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}}}||t_0,1,2,3,5,7{4,3⁶}||[[Heptipentiruncicantitruncated 8-cube]]<BR>Exiterigreatoprismated octeract||||||||||||||14192640||2580480 |- align=center BGCOLOR="#e0e0f0" !243 |<!-- [o3x3x3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}}}||t_0,1,2,3,5,6{4,3⁶}||[[Hexipentiruncicantitruncated 8-cube]]<BR>Petiterigreatoprismated octeract||||||||||||||11612160||2580480 |- align=center BGCOLOR="#e0e0f0" !244 |<!-- [x3o3o3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}}}||t_0,1,2,3,4,7{4,3⁶}||[[Heptisteriruncicantitruncated 8-cube]]<BR>Exigreatocellated octeract||||||||||||||8601600||1720320 |- align=center BGCOLOR="#e0e0f0" !245 |<!-- [o3x3o3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}}}||t_0,1,2,3,4,6{4,3⁶}||[[Hexisteriruncicantitruncated 8-cube]]<BR>Petigreatocellated octeract||||||||||||||12902400||2580480 |- align=center BGCOLOR="#e0e0f0" !246 |<!-- [o3o3x3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}}}||t_0,1,2,3,4,5{4,3⁶}||[[Pentisteriruncicantitruncated 8-cube]]<BR>Great terated octeract||||||||||||||6881280||1720320 |- align=center BGCOLOR="#f0e0e0" !247 |<!-- [x3x3x3x3x3x3x4o] -->{{dark mode invert|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,4,5,6}{3⁶,4}||[[Hexipentisteriruncicantitruncated 8-orthoplex]]<BR>Great petated diacosipentacontahexazetton||||||||||||||20643840||5160960 |- align=center BGCOLOR="#f0e0e0" !248 |<!-- [x3x3x3x3x3x3o4x] -->{{dark mode invert|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,4,5,7}{3⁶,4}||[[Heptipentisteriruncicantitruncated 8-orthoplex]]<BR>Exigreatoterated diacosipentacontahexazetton||||||||||||||23224320||5160960 |- align=center BGCOLOR="#f0e0e0" !249 |<!-- [x3x3x3x3x3o3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,4,6,7}{3⁶,4}||[[Heptihexisteriruncicantitruncated 8-orthoplex]]<BR>Exipetigreatocellated diacosipentacontahexazetton||||||||||||||23224320||5160960 |- align=center BGCOLOR="#f0e0e0" !250 |<!-- [x3x3x3x3o3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,5,6,7}{3⁶,4}||[[Heptihexipentiruncicantitruncated 8-orthoplex]]<BR>Exipetiterigreatoprismated diacosipentacontahexazetton||||||||||||||23224320||5160960 |- align=center BGCOLOR="#e0e0f0" !251 |<!-- [x3x3x3o3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,5,6,7}{4,3⁶}||[[Heptihexipentiruncicantitruncated 8-cube]]<BR>Exipetiterigreatoprismated octeract||||||||||||||23224320||5160960 |- align=center BGCOLOR="#e0e0f0" !252 |<!-- [x3x3o3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}}}||t_{0,1,2,3,4,6,7}{4,3⁶}||[[Heptihexisteriruncicantitruncated 8-cube]]<BR>Exipetigreatocellated octeract||||||||||||||23224320||5160960 |- align=center BGCOLOR="#e0e0f0" !253 |<!-- [x3o3x3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}}}||t_{0,1,2,3,4,5,7}{4,3⁶}||[[Heptipentisteriruncicantitruncated 8-cube]]<BR>Exigreatoterated octeract||||||||||||||23224320||5160960 |- align=center BGCOLOR="#e0e0f0" !254 |<!-- [o3x3x3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}}}||t_{0,1,2,3,4,5,6}{4,3⁶}||[[Hexipentisteriruncicantitruncated 8-cube]]<BR>Great petated octeract||||||||||||||20643840||5160960 |- align=center BGCOLOR="#e0f0e0" !255 |<!-- [x3x3x3x3x3x3x4x] -->{{dark mode invert|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||t_{0,1,2,3,4,5,6,7}{4,3⁶}||[[Omnitruncated 8-cube]]<BR>Great exi-octeractidiacosipentacontahexazetton||||||||||||||41287680||10321920 |}

=== The D₈ family === The D₈ family has symmetry of order 5,160,960 (8 [[factorial]] × 2⁷).

This family has 191 Wythoffian uniform polytopes, from 3 × 64 − 1 permutations of the D₈ [[Coxeter-Dynkin diagram]] with one or more rings. 127 (2 × 64 − 1) are repeated from the B₈ family and 64 are unique to this family, all listed below.

See [[list of D8 polytopes]] for Coxeter plane graphs of these polytopes.

{| class="wikitable collapsible collapsed" !colspan=15|D₈ uniform polytopes |- !rowspan=2|# !rowspan=2|[[Coxeter-Dynkin diagram]] !rowspan=2|Name {{nobold|(acronym)}}{{sfn|Klitzing}}<br />Schläfli symbol !rowspan=2|Base point<BR>(Alternately signed) !colspan=8|Element counts !rowspan=2|Circumrad |- !7||6||5||4||3||2||1||0 |- align=center !1 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}||[[8-demicube]] (hocto)<BR>h{4,3,3,3,3,3,3}||(1,1,1,1,1,1,1,1)||144||1136||4032||8288||10752||7168||1792||128||1.0000000 |- align=center !2 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}||[[Cantic 8-cube]] (thocto)<BR>h₂{4,3,3,3,3,3,3}||(1,1,3,3,3,3,3,3)|| || || || || || ||23296||3584||2.6457512 |- align=center !3 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}||Runcic 8-cube (sreho)<BR>h₃{4,3,3,3,3,3,3}||(1,1,1,3,3,3,3,3)|| || || || || || ||64512||7168||2.4494896 |- align=center !4 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}||Steric 8-cube (sapho)<BR>h₄{4,3,3,3,3,3,3}||(1,1,1,1,3,3,3,3)|| || || || || || ||98560||8960||2.2360678 |- align=center !5 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}||Pentic 8-cube (sacho)<BR>h₅{4,3,3,3,3,3,3}||(1,1,1,1,1,3,3,3)|| || || || || || ||89600||7168||1.9999999 |- align=center !6 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}||Hexic 8-cube (sotho){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/sotho.htm (x3o3o *b3o3o3o3x3o - sotho)]}}<BR>h₆{4,3,3,3,3,3,3}||(1,1,1,1,1,1,3,3)|| || || || || || ||48384||3584||1.7320508 |- align=center !7 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}||Heptic 8-cube (spuho){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/spuho.htm (x3o3o *b3o3o3o3o3x - spuho)]}}<BR>h₇{4,3,3,3,3,3,3}||(1,1,1,1,1,1,1,3)|| || || || || || ||14336||1024||1.4142135 |- align=center !8 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}||Runcicantic 8-cube (garho)<BR>h_2,3{4,3,3,3,3,3,3}||(1,1,3,5,5,5,5,5)|| || || || || || ||86016||21504||4.1231055 |- align=center !9 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}||Stericantic 8-cube (petho)<BR>h_2,4{4,3,3,3,3,3,3}||(1,1,3,3,5,5,5,5)|| || || || || || ||349440||53760||3.8729835 |- align=center !10 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}||Steriruncic 8-cube (preho)<BR>h_3,4{4,3,3,3,3,3,3}||(1,1,1,3,5,5,5,5)|| || || || || || ||179200||35840||3.7416575 |- align=center !11 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}||Penticantic 8-cube (catho)<BR>h_2,5{4,3,3,3,3,3,3}||(1,1,3,3,3,5,5,5)|| || || || || || ||573440||71680||3.6055512 |- align=center !12 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||Pentiruncic 8-cube (craho)<BR>h_3,5{4,3,3,3,3,3,3}||(1,1,1,3,3,5,5,5)|| || || || || || ||537600||71680||3.4641016 |- align=center !13 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||Pentisteric 8-cube (cepho)<BR>h_4,5{4,3,3,3,3,3,3}||(1,1,1,1,3,5,5,5)|| || || || || || ||232960||35840||3.3166249 |- align=center !14 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||Hexicantic 8-cube (totho)<BR>h_2,6{4,3,3,3,3,3,3}||(1,1,3,3,3,3,5,5)|| || || || || || ||456960||53760||3.3166249 |- align=center !15 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||Hexiruncic 8-cube (tarho)<BR>h_3,6{4,3,3,3,3,3,3}||(1,1,1,3,3,3,5,5)|| || || || || || ||645120||71680||3.1622777 |- align=center !16 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||Hexisteric 8-cube (tupho)<BR>h_4,6{4,3,3,3,3,3,3}||(1,1,1,1,3,3,5,5)|| || || || || || ||483840||53760||3 |- align=center !17 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||Hexipentic 8-cube (tucho)<BR>h_5,6{4,3,3,3,3,3,3}||(1,1,1,1,1,3,5,5)|| || || || || || ||182784||21504||2.8284271 |- align=center !18 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||Hepticantic 8-cube (putho)<BR>h_2,7{4,3,3,3,3,3,3}||(1,1,3,3,3,3,3,5)|| || || || || || ||172032||21504||3 |- align=center !19 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||Heptiruncic 8-cube (pruho)<BR>h_3,7{4,3,3,3,3,3,3}||(1,1,1,3,3,3,3,5)|| || || || || || ||340480||35840||2.8284271 |- align=center !20 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||Heptisteric 8-cube (pupaho)<BR>h_4,7{4,3,3,3,3,3,3}||(1,1,1,1,3,3,3,5)|| || || || || || ||376320||35840||2.6457512 |- align=center !21 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||Heptipentic 8-cube (pucho)<BR>h_5,7{4,3,3,3,3,3,3}||(1,1,1,1,1,3,3,5)|| || || || || || ||236544||21504||2.4494898 |- align=center !22 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||Heptihexic 8-cube (puteho)<BR>h_6,7{4,3,3,3,3,3,3}||(1,1,1,1,1,1,3,5)|| || || || || || ||78848||7168||2.236068 |- align=center !23 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||Steriruncicantic 8-cube (gapho)<BR>h_2,3,4{4,3⁶}||(1,1,3,5,7,7,7,7)|| || || || || || ||430080||107520||5.3851647 |- align=center !24 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||Pentiruncicantic 8-cube (cagreho)<BR>h_2,3,5{4,3⁶}||(1,1,3,5,5,7,7,7)|| || || || || || ||1182720||215040||5.0990195 |- align=center !25 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||Pentistericantic 8-cube (copatho)<BR>h_2,4,5{4,3⁶}||(1,1,3,3,5,7,7,7)|| || || || || || ||1075200||215040||4.8989797 |- align=center !26 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||Pentisteriruncic 8-cube (cepraho)<BR>h_3,4,5{4,3⁶}||(1,1,1,3,5,7,7,7)|| || || || || || ||716800||143360||4.7958317 |- align=center !27 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||Hexiruncicantic 8-cube (tugreho)<BR>h_2,3,6{4,3⁶}||(1,1,3,5,5,5,7,7)|| || || || || || ||1290240||215040||4.7958317 |- align=center !28 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||Hexistericantic 8-cube (tupetho)<BR>h_2,4,6{4,3⁶}||(1,1,3,3,5,5,7,7)|| || || || || || ||2096640||322560||4.5825758 |- align=center !29 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||Hexisteriruncic 8-cube (topreho)<BR>h_3,4,6{4,3⁶}||(1,1,1,3,5,5,7,7)|| || || || || || ||1290240||215040||4.472136 |- align=center !30 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||Hexipenticantic 8-cube (tucatho)<BR>h_2,5,6{4,3⁶}||(1,1,3,3,3,5,7,7)|| || || || || || ||1290240||215040||4.3588991 |- align=center !31 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||Hexipentiruncic 8-cube (tucreho)<BR>h_3,5,6{4,3⁶}||(1,1,1,3,3,5,7,7)|| || || || || || ||1397760||215040||4.2426405 |- align=center !32 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||Hexipentisteric 8-cube (tocapho)<BR>h_4,5,6{4,3⁶}||(1,1,1,1,3,5,7,7)|| || || || || || ||698880||107520||4.1231055 |- align=center !33 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||Heptiruncicantic 8-cube (pugerho)<BR>h_2,3,7{4,3⁶}||(1,1,3,5,5,5,5,7)|| || || || || || ||591360||107520||4.472136 |- align=center !34 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||Heptistericantic 8-cube (pupatho)<BR>h_2,4,7{4,3⁶}||(1,1,3,3,5,5,5,7)|| || || || || || ||1505280||215040||4.2426405 |- align=center !35 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||Heptisteriruncic 8-cube (pupraho)<BR>h_3,4,7{4,3⁶}||(1,1,1,3,5,5,5,7)|| || || || || || ||860160||143360||4.1231055 |- align=center !36 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||Heptipenticantic 8-cube (pucatho)<BR>h_2,5,7{4,3⁶}||(1,1,3,3,3,5,5,7)|| || || || || || ||1612800||215040||4 |- align=center !37 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||Heptipentiruncic 8-cube (pucarho)<BR>h_3,5,7{4,3⁶}||(1,1,1,3,3,5,5,7)|| || || || || || ||1612800||215040||3.8729835 |- align=center !38 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||Heptipentisteric 8-cube (pucapho)<BR>h_4,5,7{4,3⁶}||(1,1,1,1,3,5,5,7)|| || || || || || ||752640||107520||3.7416575 |- align=center !39 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||Heptihexicantic 8-cube (putetho)<BR>h_2,6,7{4,3⁶}||(1,1,3,3,3,3,5,7)|| || || || || || ||752640||107520||3.7416575 |- align=center !40 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||Heptihexiruncic 8-cube (putarho)<BR>h_3,6,7{4,3⁶}||(1,1,1,3,3,3,5,7)|| || || || || || ||1146880||143360||3.6055512 |- align=center !41 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||Heptihexisteric 8-cube (putopho)<BR>h_4,6,7{4,3⁶}||(1,1,1,1,3,3,5,7)|| || || || || || ||913920||107520||3.4641016 |- align=center !42 ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||Heptihexipentic 8-cube (potecho)<BR>h_5,6,7{4,3⁶}||(1,1,1,1,1,3,5,7)|| || || || || || ||365568||43008||3.3166249 |- align=center !43 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||<small>Pentisteriruncicantic 8-cube (gacho)</small><BR>h_2,3,4,5{4,3⁶}||(1,1,3,5,7,9,9,9)|| || || || || || ||1720320||430080||6.4031243 |- align=center !44 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||<small>Hexisteriruncicantic 8-cube (tugepho)</small><BR>h_2,3,4,6{4,3⁶}||(1,1,3,5,7,7,9,9)|| || || || || || ||3225600||645120||6.0827627 |- align=center !45 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||<small>Hexipentiruncicantic 8-cube (tucagreho)</small><BR>h_2,3,5,6{4,3⁶}||(1,1,3,5,5,7,9,9)|| || || || || || ||2903040||645120||5.8309517 |- align=center !46 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||<small>Hexipentistericantic 8-cube (tucpetho)</small><BR>h_2,4,5,6{4,3⁶}||(1,1,3,3,5,7,9,9)|| || || || || || ||3225600||645120||5.6568542 |- align=center !47 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||<small>Hexipentisteriruncic 8-cube (tocparho)</small><BR>h_3,4,5,6{4,3⁶}||(1,1,1,3,5,7,9,9)|| || || || || || ||2150400||430080||5.5677648 |- align=center !48 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||<small>Heptisteriruncicantic 8-cube (pugapho)</small><BR>h_2,3,4,7{4,3⁶}||(1,1,3,5,7,7,7,9)|| || || || || || ||2150400||430080||5.7445626 |- align=center !49 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||<small>Heptipentiruncicantic 8-cube (pucgreho)</small><BR>h_2,3,5,7{4,3⁶}||(1,1,3,5,5,7,7,9)|| || || || || || ||3548160||645120||5.4772258 |- align=center !50 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||<small>Heptipentistericantic 8-cube (pocpatho)</small><BR>h_2,4,5,7{4,3⁶}||(1,1,3,3,5,7,7,9)|| || || || || || ||3548160||645120||5.291503 |- align=center !51 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||<small>Heptipentisteriruncic 8-cube (pocpreho)</small><BR>h_3,4,5,7{4,3⁶}||(1,1,1,3,5,7,7,9)|| || || || || || ||2365440||430080||5.1961527 |- align=center !52 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||<small>Heptihexiruncicantic 8-cube (putagreho)</small><BR>h_2,3,6,7{4,3⁶}||(1,1,3,5,5,5,7,9)|| || || || || || ||2150400||430080||5.1961527 |- align=center !53 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||<small>Heptihexistericantic 8-cube (putapatho)</small><BR>h_2,4,6,7{4,3⁶}||(1,1,3,3,5,5,7,9)|| || || || || || ||3870720||645120||5 |- align=center !54 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||<small>Heptihexisteriruncic 8-cube (poteparho)</small><BR>h_3,4,6,7{4,3⁶}||(1,1,1,3,5,5,7,9)|| || || || || || ||2365440||430080||4.8989797 |- align=center !55 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipenticantic 8-cube (potacotho)</small><BR>h_2,5,6,7{4,3⁶}||(1,1,3,3,3,5,7,9)|| || || || || || ||2580480||430080||4.7958317 |- align=center !56 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipentiruncic 8-cube (potcarho)</small><BR>h_3,5,6,7{4,3⁶}||(1,1,1,3,3,5,7,9)|| || || || || || ||2795520||430080||4.6904159 |- align=center !57 ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipentisteric 8-cube (potcapho)</small><BR>h_4,5,6,7{4,3⁶}||(1,1,1,1,3,5,7,9)|| || || || || || ||1397760||215040||4.5825758 |- align=center !58 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||<small>Hexipentisteriruncicantic 8-cube (gotho)</small><BR>h_2,3,4,5,6{4,3⁶}||(1,1,3,5,7,9,11,11)|| || || || || || ||5160960||1290240||7.1414285 |- align=center !59 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||<small>Heptipentisteriruncicantic 8-cube (pugecho)</small><BR>h_2,3,4,5,7{4,3⁶}||(1,1,3,5,7,9,9,11)|| || || || || || ||5806080||1290240||6.78233 |- align=center !60 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||<small>Heptihexisteriruncicantic 8-cube (potegapho)</small><BR>h_2,3,4,6,7{4,3⁶}||(1,1,3,5,7,7,9,11)|| || || || || || ||5806080||1290240||6.480741 |- align=center !61 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipentiruncicantic 8-cube (potcograho)</small><BR>h_2,3,5,6,7{4,3⁶}||(1,1,3,5,5,7,9,11)|| || || || || || ||5806080||1290240||6.244998 |- align=center !62 ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipentistericantic 8-cube (potcupetho)</small><BR>h_2,4,5,6,7{4,3⁶}||(1,1,3,3,5,7,9,11)|| || || || || || ||6451200||1290240||6.0827627 |- align=center !63 ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||<small>Heptihexipentisteriruncic 8-cube (potcoparho)</small><BR>h_3,4,5,6,7{4,3⁶}||(1,1,1,3,5,7,9,11)|| || || || || || ||4300800||860160||6.0000000 |- align=center !64 ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>= {{nowrap|{{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}}}||<small>Heptihexipentisteriruncicantic 8-cube (gupho)</small><BR>h_2,3,4,5,6,7{4,3⁶}||(1,1,3,5,7,9,11,13)|| || || || || || ||2580480||10321920||7.5498347 |}

=== The E₈ family === The E₈ family has symmetry order 696,729,600.

There are 255 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. Eight forms are shown below, 4 single-ringed, 3 truncations (2 rings), and the final omnitruncation are given below. Bowers-style acronym names are given for cross-referencing.

See also [[list of E8 polytopes]] for Coxeter plane graphs of this family.

{| class="wikitable collapsible collapsed" !colspan=15|E₈ uniform polytopes |- !rowspan=2|# !rowspan=2|[[Coxeter-Dynkin diagram]]<br/> !rowspan=2|Names !colspan=8|Element counts |- ! 7-faces ! 6-faces ! 5-faces ! 4-faces ! Cells ! Faces ! Edges ! Vertices |- align=center |1||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Gosset 4 21 polytope|4₂₁]] (fy) |19440||207360||483840||483840||241920||60480||6720||240 |- align=center |2||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Truncated 4 21 polytope|Truncated 4₂₁]] (tiffy) | || || || || || ||188160||13440 |- align=center |3||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Rectified 4 21 polytope|Rectified 4₂₁]] (riffy) |19680||375840||1935360||3386880||2661120||1028160||181440||6720 |- align=center |4||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Birectified 4 21 polytope|Birectified 4₂₁]] (borfy) |19680||382560||2600640||7741440||9918720||5806080||1451520||60480 |- align=center |5||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||[[Trirectified 4 21 polytope|Trirectified 4₂₁]] (torfy) |19680||382560||2661120||9313920||16934400||14515200||4838400||241920 |- align=center |6||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||[[Rectified 1 42 polytope|Rectified 1₄₂]] (buffy) |19680||382560||2661120||9072000||16934400||16934400||7257600||483840 |- align=center |7||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||[[Rectified 2 41 polytope|Rectified 2₄₁]] (robay) |19680||313440||1693440||4717440||7257600||5322240||1451520||69120 |- align=center |8||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||[[2 41 polytope|2₄₁]] (bay) |17520||144960||544320||1209600||1209600||483840||69120||2160 |- align=center |9||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||[[Truncated 2 41 polytope|Truncated 2₄₁]] | || || || || || || ||138240 |- align=center |10||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||[[1 42 polytope|1₄₂]] (bif) |2400||106080||725760||2298240||3628800||2419200||483840||17280 |- align=center |11||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||[[Truncated 1 42 polytope|Truncated 1₄₂]] | || || || || || || ||967680 |- align=center |12||{{nowrap|{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}}}||[[Omnitruncated 4 21 polytope|Omnitruncated 4₂₁]] | || || || || || || ||696729600 |}

== Regular and uniform honeycombs == [[File:Coxeter diagram affine rank8 correspondence.png|518px|thumb|Coxeter-Dynkin diagram correspondences between families and higher symmetry within diagrams. Nodes of the same color in each row represent identical mirrors. Black nodes are not active in the correspondence.]] There are five fundamental affine [[Coxeter groups]] that generate regular and uniform tessellations in 7-space: {| class="wikitable" |- !# !colspan=2|[[Coxeter group]] ![[Coxeter diagram]] !Forms |- align=center |1||<math>{\tilde{A}}_7</math>||[3^[8]]||{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}||29 |- align=center |2||<math>{\tilde{C}}_7</math>||[4,3⁵,4]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|4|node}}||135 |- align=center |3||<math>{\tilde{B}}_7</math>||[4,3⁴,3^1,1]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|4|node}}||191 (64 new) |- align=center |4||<math>{\tilde{D}}_7</math>||[3^1,1,3³,3^1,1]||{{CDD|nodes|split2|node|3|node|3|node|3|node|split1|nodes}}||77 (10 new) |- align=center |5||<math>{\tilde{E}}_7</math>||[3^3,3,1]||{{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node}}||143 |}

Regular and uniform tessellations include: * <math>{\tilde{A}}_7</math> 29 uniquely ringed forms, including: ** [[7-simplex honeycomb]]: {3^[8]} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}} * <math>{\tilde{C}}_7</math> 135 uniquely ringed forms, including: ** Regular [[7-cube honeycomb]]: {4,3⁴,4} = {4,3⁴,3^1,1}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|4|node}} = {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|split1|nodes}} *<math>{\tilde{B}}_7</math> 191 uniquely ringed forms, 127 shared with <math>{\tilde{C}}_7</math>, and 64 new, including: ** [[7-demicube honeycomb]]: h{4,3⁴,4} = {3^1,1,3⁴,4}, {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|4|node}} = {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|4|node}} * <math>{\tilde{D}}_7</math>, [3^1,1,3³,3^1,1]: 77 unique ring permutations, and 10 are new, the first Coxeter called a [[quarter 7-cubic honeycomb]]. ** {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|split1|nodes_10lu}} * <math>{\tilde{E}}_7</math> 143 uniquely ringed forms, including: ** [[1 33 honeycomb|1₃₃ honeycomb]]: {3,3^3,3}, {{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node_1}} ** [[3 31 honeycomb|3₃₁ honeycomb]]: {3,3,3,3^3,1}, {{CDD|nodes_10r|3ab|nodes|3ab|nodes|split2|node|3|node}}

=== Regular and uniform hyperbolic honeycombs === There are no compact hyperbolic Coxeter groups of rank 8, groups that can generate honeycombs with all finite facets, and a finite [[vertex figure]]. However, there are [[Coxeter-Dynkin diagram#Rank 4 to 10|4 paracompact hyperbolic Coxeter groups]] of rank 8, each generating uniform honeycombs in 7-space as permutations of rings of the Coxeter diagrams.

{| class=wikitable |align=right|<math>{\bar{P}}_7</math> = [3,3^[7]]:<BR>{{CDD|branch|3ab|nodes|3ab|nodes|split2|node|3|node}} |align=right|<math>{\bar{Q}}_7</math> = [3^1,1,3²,3^2,1]:<BR> {{CDD|nodea|3a|branch|3a|nodea|3a|branch|3a|nodea|3a|nodea}} |align=right|<math>{\bar{S}}_7</math> = [4,3³,3^2,1]:<BR> {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|4a|nodea}} |align=right|<math>{\bar{T}}_7</math> = [3^3,2,2]:<BR>{{CDD|nodes|3ab|nodes|split2|node|3|node|3|node|3|node}} |}

== References == {{reflist}} * [[Thorold Gosset|T. Gosset]]: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', [[Messenger of Mathematics]], Macmillan, 1900 * {{cite journal|year=1910|author=A. Boole Stott|authorlink=Alicia Boole Stott|title=Geometrical deduction of semiregular from regular polytopes and space fillings|journal=Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam.|volume=XI|number=1|publisher=Johannes Müller|location=Amsterdam|url=https://dwc.knaw.nl/DL/publications/PU00011492.pdf|archive-url=https://web.archive.org/web/20250429000816/https://dwc.knaw.nl/DL/publications/PU00011492.pdf|archive-date=29 April 2025}} * [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]: ** H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: ''Uniform Polyhedra'', Philosophical Transactions of the Royal Society of London, 1954 ** H.S.M. Coxeter, ''Regular Polytopes'', 3rd edition, Dover, New York, 1973 ** '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, [https://www.wiley.com/en-us/Kaleidoscopes-p-9780471010036 wiley.com], {{isbn|978-0-471-01003-6}} *** (Paper 22) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes I'', [Math. Zeit. 46 (1940) 380–407, MR 2,10] *** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559–591] *** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3–45] * [[Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966 * {{KlitzingPolytopes|polyzetta.htm|8D uniform polytopes (polyzetta) with acronyms}} {{sfn whitelist| CITEREFKlitzing}}

== External links == * [http://www.steelpillow.com/polyhedra/ditela.html Polytope names] * [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions] * [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

{{DEFAULTSORT:8-Polytope}} [[Category:8-polytopes]]