Cube Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. 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. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces
Compound of 5-cube and 5-orthoplex cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa. It can be seen as the 5-dimensional analogue of a compound of cube and octahedron. The 42 Cartesian coordinates of the vertices of the compound are. The convex hull of the vertices makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound can be seen in projection as the union of the two polytope graphs. The convex hulll as the dual of the rectified 5-orthoplex will have the same vertices, but