# The Parametrized Szilassi Polyhedron

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The following steps construct a regular toroid with seven faces, the Szilassi polyhedron.

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Contributed by: Lajos Szilassi (University of Szeged, Hungary) and Sándor Kabai (May 2008)

Open content licensed under CC BY-NC-SA

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## Details

The Szilassi polyhedron is a polyhedral realization of a regular map (namely, the Heawood map).

Recall the classical definition [1]:

"A map is said to be regular if its automorphism group contains two particular automorphisms: one, say , which cyclically permutes the edges that are successive sides of one face, and another, say , which cyclically permutes the successive edges meeting at one vertex of this face."

Reference

[1] H. S. M. Coxeter and W. O. Moser, *Generators and Relations for Discrete Groups*, Berlin: Springer-Verlag, 1972 pp. 101–102.

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