Szilassi Polyhedron

The Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with 14 vertices, 21 edges, and 7 hexagonal faces. It was discovered by the Hungarian mathematician Lajos Szilassi in 1977. About that time it was described - probably independently - by Martin Gardner in his Scientific American column. (The article has been included in one of his later collections. At a later time, he gave credit to Szilassi for the discovery of the polyhedron.)

It is the dual of the Császár polyhedron. Both are of the toroidal family, with a single hole. The Szilassi polyhedron is remarkable in that all seven faces are adjacent to each other such that it takes 7 colors to paint its faces so that no adjacent two have the same color.

What if applet does not run?

Drag the mouse to rotate the prism. Use the right button to remove and put back individual faces.

(Acknowledgement: I have learned most of Java details from the implementation by Meiko Rachimow. I found the geometry of the solid at the software3d online forum.)

References

  1. M. Gardner, Time Travel and Other Mathematical Bewilderments, W.H.Freeman and Co., NY, 1988.
  2. M. Gardner, Fractal Music, Hypercards and More ..., W.H.Freeman and Co., NY, 1991.

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