Holyhedron - Printable Version +- MKLab (https://mklab.gr) +-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1) +--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3) +---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13) +---- Thread: Holyhedron (/showthread.php?tid=1001)

Holyhedron - mklabgr - 07-09-2026 Holyhedron Summary A holyhedron is a remarkable object in geometry and polyhedron theory: a three-dimensional polyhedron in which every face contains at least one polygon-shaped hole, with each hole completely separated from both the face's outer boundary and any other holes. The idea was introduced by mathematician John H. Conway, while the playful name "holyhedron"—a pun on "holy" and "holes"—was coined by David W. Wilson in 1997. Conway challenged mathematicians to determine whether such a figure could actually exist, even offering a cash prize that decreased as the number of faces increased, encouraging the search for increasingly elegant constructions.  For several years, the existence of a holyhedron remained an open mathematical problem until Jade P. Vinson produced the first valid construction in 1999. Although mathematically sound, it required an astonishing 78,585,627 faces, demonstrating that the concept was possible but far from practical. A few years later, Don Hatch dramatically improved the result by designing a holyhedron with just 492 faces, significantly advancing the search for simpler examples.  More recently, researchers have continued refining these constructions, highlighting that the minimum possible number of faces remains an intriguing unsolved problem in computational geometry and mathematical research. The story of the holyhedron illustrates how seemingly playful questions can inspire deep mathematical discoveries, pushing the boundaries of geometric thinking and proving that even the most unusual ideas can lead to meaningful advances.  ARTICLE