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Holyhedron


A holyhedron is a polyhedron in which every face contains at least one hole whose boundary shares no point with the outer boundary of that face. The faces and their holes are bounded by finite-sided polygons. D. Wilson coined the term in 1997, although no actual holyhedron was known until 1999, when a holyhedron with 78585627 faces was constructed (Vinson 2000).

J. H. Conway believes that the minimal number of faces should be closer to 100, and offered a prize of $10000 divided by the number of faces for a better solution. A holyhedron with 492 faces was subsequently discovered, good for a prize of $20.33 (Hatch).


See also

Polyhedron

Portions of this entry contributed by Ed Pegg, Jr. (author's link)

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References

Hatch, D. "Holyhedron!" https://www.plunk.org/~hatch/Holyhedron/.Vinson, J. "On Holyhedra." Disc. Comput. Geom. 24, 85-104, 2000.

Referenced on Wolfram|Alpha

Holyhedron

Cite this as:

Weisstein, Eric W., with contributions by Ed Pegg, Jr.. "Holyhedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Holyhedron.html

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