The Platonic solids are convex polyhedra with equivalent faces composed of congruent convex regular polygons meeting at equivalent vertices. They are sometimes also called the regular solids or regular polyhedra, although some authors use this term to refer to more a more general class including the Kepler-Poinsot solids. There are exactly five Platonic solids (Steinhaus 1999, pp. 252-256): the cube, dodecahedron, icosahedron, octahedron, and tetrahedron, as was proved by Euclid in the last proposition of the Elements.

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