{{Short description|Type of 3-dimensional geometric body}} {{multiple image | image1 = Holyhedra, outer view.png | image2 = Holyhedra - Inner view.png | footer = 492 face Holyhedron for outer view, and with some pieces removed for inner view | total_width = 400 }} {{unsolved|mathematics|What is the lowest number of faces possible for a holyhedron?}} In mathematics, a '''holyhedron''' is a type of 3-dimensional geometric body: a polyhedron each of whose faces contains at least one polygon-shaped hole, and whose holes' boundaries share no point with each other or the face's boundary.{{r|vinson}}
== History == The concept was first introduced by John H. Conway; the term "holyhedron" was coined by David W. Wilson in 1997 as a pun involving polyhedra and holes. Conway also offered a prize of 10,000 USD, divided by the number of faces, for finding an example, asking:{{r|do}} {{blockquote|Is there a polyhedron in Euclidean three-dimensional space that has only finitely many plane faces, each of which is a closed connected subset of the appropriate plane whose relative interior in that plane is multiply connected?}}
No actual holyhedron was constructed until 1999, when Jade P. Vinson presented an example of a holyhedron with a total of 78,585,627 faces.{{r|peterson|vinson}} Another example was subsequently given by Don Hatch, who presented a holyhedron with 492 faces in 2003, worth about 20.33 USD prize money.{{r|hatch}} A new construction was obtained by Geby Jaff using Archivara in 2026, containing 476 faces.<ref>{{Cite web |url=https://github.com/spicylemonade/holyhedron/tree/main |title=GitHub - spicylemonade/holyhedron: What is the lowest number of faces possible for a holyhedron? beat 492 |website=GitHub |access-date=2026-04-02}}</ref>
== References == <references>
<ref name=do>{{cite journal | last1 = Demaine | first1 = Erik D. | last2 = O'Rourke | first2 = Joseph | year = 1999 | doi = 10.1145/333623.333625 | issue = 3 | journal = ACM SIGACT News | pages = 39–42 | title = Computational geometry column 37 | volume = 30 | s2cid = 9358750 }}</ref>
<ref name=hatch>{{cite web | last = Hatch | first = Don | year = 2003 | title = Holyhedron! | url = http://www.plunk.org/~hatch/Holyhedron/ }}</ref>
<ref name=peterson>{{cite news | last = Peterson | first = Ivars | title = Punctured Polyhedra | url= https://www.sciencenews.org/article/punctured-polyhedra | magazine = Science News | date = December 11, 2002 | archive-url = https://web.archive.org/web/20160304113733/https://www.sciencenews.org/article/punctured-polyhedra | archive-date = March 4, 2016 }}</ref>
<ref name=vinson>{{cite journal | last = Vinson | first = J. | doi = 10.1007/s004540010033 | issue = 1 | journal = Discrete & Computational Geometry | mr = 1765235 | pages = 85–104 | title = On holyhedra | volume = 24 | year = 2000 | doi-access = free }}</ref>
</references>
Category:Polyhedra Category:John Horton Conway