# 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

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

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