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