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In 1861, A. F. Möbius showed that a complete graph with seven vertices can be drawn on the surface of a torus. Any two vertices of this graph are connected by a single edge and no edges intersect.

In 1949, Á. Császár, in response to a problem presented for a mathematical competition for secondary school students, constructed a polyhedron having no intersecting faces, whose combinatorial structure is a Möbius torus (Cs0).

In 1985, L. Szilassi, while producing a less compact version (Cs1) of the polyhedron Cs0, found a "visibly" different version, which can be produced by continuously moving the coordinates of the points, where the faces of the polyhedron get intersected by one another (Cs3).

In 1986, J. Bokowski proved that the Császár polyhedron has four visibly different versions with the same combinatorial structure. He also confirmed that no other versions exists. Cs2 and Cs4 were constructions by Bokowski.

For more information, visit any of the following links:

http://www.mi.sanu.ac.rs/vismath/visbook/csaszar/index.html

http://upcommons.upc.edu/revistes/bitstream/2099/1038/1/st13-06-a3-ocr.pdf

http://upcommons.upc.edu/revistes/bitstream/2099/1067/1/st17-10-a7-ocr.pdf

http://www.eg-models.de/models/Classical_Models/2001.02.069/_direct_link.html

http://dmccooey.com/polyhedra/Csaszar1.html