Nets for the Császár Polyhedra

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A Császár polyhedron is a nonconvex polyhedron, topologically equivalent to a toroid, with 14 triangular faces. This polyhedron has no diagonals, every pair of vertices being connected by an edge (in common with the tetrahedron). The Császár polyhedron has four visibly different versions. This Demonstration illustrates each version and its net.

Contributed by: Lajos Szilassi (University of Szeged, Hungary) and Izidor Hafner (May 2016)
Additional contribution by: Sándor Kabai
Open content licensed under CC BY-NC-SA




[1] L. Szilassi, "Regular Toroids," Structural Topology, Quebec: Université de Montréal, 13, 1986 pp. 69–80.

[2] L. Szilassi, "On Three Classes of Regular Toroids," Symmetry: Culture and Science, 11(1–4), 2000 pp. 317–335.

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