A toroidal polyhedron is a Polyhedron with Genus (i.e., having one or more Holes). Examples of toroidal polyhedra include the Császár Polyhedron and Szilassi Polyhedron, both of which have Genus 1 (i.e., the Topology of a Torus).

The only known Toroidal Polyhedron with no Diagonals is the Császár Polyhedron. If another exists, it must have 12 or more Vertices and Genus . The smallest known single-hole toroidal Polyhedron made up of only Equilateral Triangles is composed of 48 of them.

**References**

Gardner, M. *Time Travel and Other Mathematical Bewilderments.* New York: W. H. Freeman, p. 141, 1988.

Hart, G. ``Toroidal Polyhedra.'' http://www.li.net/~george/virtual-polyhedra/toroidal.html.

Stewart, B. M. *Adventures Among the Toroids, 2nd rev. ed.* Okemos, MI: B. M. Stewart, 1984.

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1999-05-26