{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|Grand 120-cell |- |bgcolor=#ffffff align=center colspan=2|280px<BR>Orthogonal projection |- |bgcolor=#e7dcc3|Type||Schläfli-Hess polytope |- |bgcolor=#e7dcc3|Cells||120 {5,3} |- |bgcolor=#e7dcc3|Faces||720 {5} |- |bgcolor=#e7dcc3|Edges||720 |- |bgcolor=#e7dcc3|Vertices||120 |- |bgcolor=#e7dcc3|Vertex figure||{3,5/2} |- |bgcolor=#e7dcc3|Schläfli symbol|| {5,3,5/2} |- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram||{{CDD|node_1|5|node|3|node||rat|d2|node}} |- |bgcolor=#e7dcc3|Symmetry group||H<sub>4</sub>, [3,3,5] |- |bgcolor=#e7dcc3|Dual|| Great stellated 120-cell |- |bgcolor=#e7dcc3|Properties|| Regular |} In geometry, the '''grand 120-cell''' or '''grand polydodecahedron''' is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes.

It is one of four ''regular star 4-polytopes'' discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.

==Related polytopes== It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell. {| class="wikitable" width=600 |+ Orthographic projections by Coxeter planes |- align=center !H<sub>4</sub> ! - !F<sub>4</sub> |- align=center |200px<BR>[30] |200px<BR>[20] |200px<BR>[12] |- align=center !H<sub>3</sub> !A<sub>2</sub> / B<sub>3</sub> / D<sub>4</sub> !A<sub>3</sub> / B<sub>2</sub> |- align=center |200px<BR>[10] |200px<BR>[6] |200px<BR>[4] |} It could be seen as another 4D analogue of the three-dimensional great dodecahedron due to being a pentagonal polytope with enlarged facets.

==See also== *List of regular polytopes *Convex regular 4-polytope *Kepler-Poinsot solids - regular star polyhedron *Star polygon - regular star polygons

==References== *Edmund Hess, (1883) ''Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder'' [http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=ABN8623.0001.001]. *H. S. M. Coxeter, ''Regular Polytopes'', 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}. *John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008, {{ISBN|978-1-56881-220-5}} (Chapter 26, Regular Star-polytopes, pp.&nbsp;404–408) * {{KlitzingPolytopes|polychora.htm|4D uniform polytopes (polychora)|o5o3o5/2x - gahi}}

==External links== *[http://hometown.aol.com/hedrondude/regulars.html Regular polychora] {{Webarchive|url=https://web.archive.org/web/20030906012615/http://hometown.aol.com/hedrondude/regulars.html |date=2003-09-06 }} *[http://mathforum.org/library/drmath/view/54786.html Discussion on names] *[https://web.archive.org/web/20061107052613/http://www.mathematik.uni-regensburg.de/Goette/sterne/ Reguläre Polytope] *[https://web.archive.org/web/20070704012333/http://davidf.faricy.net/polyhedra/Star_Polychora.html The Regular Star Polychora]

{{Regular 4-polytopes}}

Category:Regular 4-polytopes {{polychora-stub}}