# Szilassi polyhedron
A toroidal heptahedron (seven-sided polygon) first described in 1977 by
the Hungarian mathematician Lajos Szilassi. It has 7 faces, 14 vertices,
21 edges, and 1 hole. The Szilassi polyhedron is the dual
of the Császár polyhedron and,
like it, shares with the tetrahedron
the property that each of its faces touches all the other faces. Whereas
a tetrahedron demonstrates that four colors are necessary for a map on a
surface topologically equivalent to a sphere, the Szilassi and Császár polyhedra
show that seven colors are necessary for a map on a surface topologically
equivalent to a torus. ## Related
category
• SOLIDS
AND SURFACES |