Holyhedron
Type of 3-dimensional geometric body
title: "Holyhedron" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["polyhedra", "john-horton-conway"] description: "Type of 3-dimensional geometric body" topic_path: "general/polyhedra" source: "https://en.wikipedia.org/wiki/Holyhedron" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Type of 3-dimensional geometric body ::
| 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 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.
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:
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. Another example was subsequently given by Don Hatch, who presented a holyhedron with 492 faces in 2003, worth about 20.33 USD prize money.
References
| 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
| last = Hatch | first = Don | year = 2003 | title = Holyhedron! | url = http://www.plunk.org/~hatch/Holyhedron/
| 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
| 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
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