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The cube is the only regular hexahedron and is one of the five Platonic solids . It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped , an equilateral cuboid and a right rhombohedron . It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron .
The unique regular hexahedron is the cube, and there are two hexahedra that can be built from regular polygons with equal edge lengths: the regular triangular dipyramid the pentagonal pyramid. Through graph duality, the list of numbers of vertices for each polyhedron in a hexahedron corresponds to the degree sequence (sequence of vertex degrees) of a hexahedral graph. The following table lists the hexahedra, together with their degree sequences, number of vertices , and number of edges , which are related through the polyhedral formula.