Szilassi Polyhedron
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.
The skeleton of the Szilassi polyhedron is equivalent to the Heawood graph, shown above.
See also
Császár Polyhedron, Heawood Graph, Toroidal Polyhedron, Torus ColoringExplore with Wolfram|Alpha
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References
Ace, T. "Szilassi Polyhedron." https://www.minortriad.com/szilassi.html.Eppstein, D. "Polyhedra and Polytopes." https://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." https://www.georgehart.com/virtual-polyhedra/toroidal.html.Knuth, D. E. §7.2.2.3 in The Art of Computer Programming, Vol. 4. Pre-Fascicle 7A, pp. 9-11 and 14, Dec. 5, 2024.Knuth, D. E. Ex. 36 and 45, §7.2.2.3 in The Art of Computer Programming, Vol. 4. Pre-Fascicle 7A, p. 116 and 117, Dec. 5, 2024.Referenced on Wolfram|Alpha
Szilassi PolyhedronCite this as:
Weisstein, Eric W. "Szilassi Polyhedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SzilassiPolyhedron.html