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