Császár polyhedron

The Császár polyhedron is a non- convex polyhedron with a hole, consisting of 14 triangular sides, 21 edges and 7 corners. It has no diagonals and, besides the tetrahedron, is the only known polyhedron with this property (with the additional requirement of being the edge of a manifold). Each pair of corners is connected by an edge.

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Rotationally symmetrical 3D model with torus

The polyhedron has the topology of a torus ( Euler characteristic ) ${\displaystyle \chi =0}$

It was introduced by Ákos Császár in 1949 .

It is dual to the Szilassi polyhedron .

Web links

• Eric Weisstein: Csaszar Polyhedron, Mathworld
• Folding plan by Sascha Rogmann

Individual evidence

1. ↑ Otherwise there are other examples. Sándor Szabó Polyhedra without diagonals , Periodica Mathematica Hungarica 15, 1984, pp. 41–49, Part 2, Periodica Mathematica Hungarica 58, 2009, 181–187
2. ↑ Csaszar: A Polyhedron Without Diagonals, Acta Sci. Math. (Szeged) 13 (1949), 140-142