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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 .
More generally, an octahedron can be any polyhedron with eight faces. The regular octahedron has 6 vertices and 12 edges, the minimum for an octahedron; nonregular octahedra may have as many as 12 vertices and 18 edges. [1] Other nonregular octahedra include the following.1  Hexagonal prism: Two faces are parallel regular hexagons; six squares link corresponding pairs of hexagon edges.n octahedron can be placed with its center at the origin and its vertices on the coordinate axes; the Cartesian coordinates of the vertices are then.