Szilassi polyhedron

The Szilassi - polyhedron is a non-convex polyhedron with a hole and seven hexagonal sides, two sides have a common edge. It has 21 edges and 14 vertices.

It has the topology of a torus ( Euler characteristic, genus g = 1) and provides an example of a polyhedron in which the full complement of seven colors are required ( by the theorem of Ringel- Youngs ) to the map coloring.

It is next to the tetrahedron, the only known polyhedron, where each page with every other page has a common edge.

The polyhedron was discovered in 1977 by the Hungarian mathematician Lajos Szilassi ( b. 1942 ). It is dual to the 1949 discovered Csaszar polyhedron.