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A Polyhedron topologically equivalent to a Torus discovered in the late 1940s.  It has 7
Vertices, 14 faces, and 21 Edges, and is the Dual
Polyhedron of the Szilassi Polyhedron.  Its Skeleton is Isomorphic to the
Complete Graph 
.
See also Szilassi Polyhedron, Toroidal Polyhedron
References
Császár, Á.  ``A Polyhedron without Diagonals.'' Acta Sci. Math. 13, 140-142, 1949-1950.
 
Gardner, M.  ``The Császár Polyhedron.''  Ch. 11 in Time Travel and Other Mathematical Bewilderments.
  New York: W. H. Freeman, 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.li.net/~george/virtual-polyhedra/toroidal.html.