High Quality Content by WIKIPEDIA articles! The Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. Each face of this polyhedron shares an edge with each other face. As a result, it requires seven colours to colour each adjacent face, providing the lower bound for the seven colour theorem. It has an axis of 180-degree symmetry; three pairs of faces are congruent leaving one unpaired hexagon that has the same rotational symmetry as the polyhedron. The 14 vertices and 21 edges of the Szilassi polyhedron form an embedding of the Heawood graph onto the surface of a torus.

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