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Császár Polyhedron


CsaszarCsaszarNet

The Császár polyhedron is a polyhedron that is topologically equivalent to a torus which was discovered in the late 1940s by Ákos Császár (Gardner 1975). It has 7 polyhedron vertices, 14 faces, and 21 polyhedron edges, and is the dual polyhedron of the Szilassi polyhedron.

CompleteGraphK7

The skeleton of the Császár polyhedron, illustrated above, is isomorphic to the complete graph K_7. Rather surprisingly, the graph of the Császár polyhedron's skeleton and its dual graph can be used to find Steiner triple systems (Gardner 1975).

CsaszarConstruction

The figure above shows how to construct the Császár polyhedron.


See also

Szilassi Polyhedron, Toroidal Polyhedron

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References

Császár, Á. "A Polyhedron without Diagonals." Acta Sci. Math. 13, 140-142, 1949-1950.Gardner, M. "Mathematical Games: On the Remarkable Császár Polyhedron and Its Applications in Problem Solving." Sci. Amer. 232, 102-107, May 1975.Gardner, M. "The Császár Polyhedron." Ch. 11 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 139-152, 1988.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. "Császár Polyhedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CsaszarPolyhedron.html

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