In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another with equivalent edges. So the regular polyhedra — the Platonic solids and Kepler-Poinsot polyhedra-are arranged into dual pairs, with the exception of the regular tetrahedron which is self-dual.

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