Szilassi polyhedron

from Wikipedia, the free encyclopedia

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

Szilassi polyhedron
Animated Szilassi polyhedron

It has the topology of a torus ( Euler characteristic , gender ) and provides an example of a polyhedron in which the full number of seven colors (according to the Ringel-Youngs theorem ) are necessary to color the card.

Besides the tetrahedron, it is the only known polyhedron in which every side has a common edge with every other side.

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

literature

  • Martin Gardner , Mathematical Games: In Which a Mathematical Aesthetic is Applied to Modern Minimal Art, Scientific American, November 1978

Web links

Individual evidence

  1. Lajos Szilassi Regular toroids , Structural Topology 13, 1986, pp. 69-80