September 8, 2015

Polyhedron with a Hole

The Szilassi polyhedron forms the basis for a four-bulb glass lamp, created by Hans Schepker.

This intriguing polyhedron was discovered in 1977 by Hungarian mathematician Lajos Szilassi. It has seven faces, 14 vertexes, 21 edges, and a hole. Each face is a six-sided polygon. Topologically, if it were smoothed out, it would be equivalent to a doughnut (or torus). You could describe it as a toroidal heptahedron.

Like the tetrahedron, the Szilassi polyhedron has the remarkable property that each of its faces touches all the other faces.

Photos by I. Peterson

1 comment:

drmathochist said...

That last fact, that each face touches each other face, proves that genus-1 maps are NOT four-colorable!