A holyhedron is polyhedron whose faces and holes are all finite-sided polygons and that contains at least one hole whose boundary shares no point with a face boundary. 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).

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

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Hatch, D. "Holyhedron!", J. "On Holyhedra." Disc. Comput. Geom. 24, 85-104, 2000.

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Cite this as:

Pegg, Ed Jr. and Weisstein, Eric W. "Holyhedron." From MathWorld--A Wolfram Web Resource.

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