Cube have octahedral symmetry. The cube is a part of a sequence of rhombic polyhedra and tilings with ["n",3] Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are squares. The cube is a square prism: As a trigonal trapezohedron, the cube is related to the hexagonal dihedral symmetry family. It is an element of 9 of 28 convex uniform honeycombs: It is also an element of five four-dimensional uniform polychora: The skeleton of the cube (the vertices and edges) form a graph, with 8 vertices, and 12 edges. It is a special case of
Folded cube graph nearly the same vertex degree but only half the diameter. Efficient distributed algorithms (relative to those for a "hypercube") are known for broadcasting information in a folded cube. Folded cube graph In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects "opposite" pairs of hypercube vertices. The folded cube graph of order "k" (containing 2 vertices) may be formed by adding edges between opposite pairs of vertices in a hypercube graph of order "k" − 1. (In a hypercube with 2 vertices, a pair of