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Szilassi Polyhedron


SzilassiSzilassiPolyhedron
SzilassiPolyhedronNet

The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every pair of faces has a polygon edge in common. The Szilassi polyhedron has 14 polyhedron vertices, seven faces, and 21 polyhedron edges, and is the dual polyhedron of the Császár polyhedron. This polyhedron was discovered by L. Szilassi in 1977. In the above illustration of the net, sides indicated by letters are connected with the corresponding side indicated by the same letter but with a different number of primes. Like the tetrahedron, each face of the Szilassi polyhedron touches all other faces.

HeawoodGraph

The skeleton of the Szilassi polyhedron is equivalent to the Heawood graph, shown above.


See also

Császár Polyhedron, Heawood Graph, Toroidal Polyhedron, Torus Coloring

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References

Ace, T. "Szilassi Polyhedron." http://www.minortriad.com/szilassi.html.Eppstein, D. "Polyhedra and Polytopes." http://www.ics.uci.edu/~eppstein/junkyard/polytope.html.Gardner, M. "Mathematical Games: In Which a Mathematical Aesthetic is Applied to Modern Minimal Art." Sci. Amer. 239, 22-32, Nov. 1978.Gardner, M. Fractal Music, Hypercards, and More Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 118-120, 1992.Hart, G. "Toroidal Polyhedra." http://www.georgehart.com/virtual-polyhedra/toroidal.html.

Cite this as:

Weisstein, Eric W. "Szilassi Polyhedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SzilassiPolyhedron.html

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