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Toroidal polyhedra

Polyhedra with the topological type of a torus are called toroidal polyhedra, and have Euler characteristic V − E + F = 0. For any number of holes, the formula generalizes to V − E + F = 2 − 2 N, where N is the number of holes.

The term "toroidal polyhedron" is also used for higher-genus polyhedra and for immersions of toroidal polyhedra.