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
Rubik's Cube group define orientation. One choice is the following group, given by generators (the last generator is a 3 cycle on the edges): Since "C" is a normal subgroup and the intersection of "C" and "C" is the identity and their product is the whole cube group, it follows that the cube group "G" is the semi-direct product of these two groups. That is Next we can take a closer look at these two groups. The structure of "C" is since the group of rotations of each corner (resp. edge) cube is formula_30 (resp. formula_31), and in each case all but one