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 as many vertices, by identifying together (or contracting) every opposite pair of vertices. An order-"k" folded cube graph is "k"-regular with 2 vertices and 2"k" edges. The chromatic number of the order-"k" folded cube graph is two when "k" is even (that is, in this case, the graph is bipartite) and four when "k" is odd. The odd girth of a folded cube of odd order is "k", so for odd "k" greater than three the folded cube graphs provide a class of triangle-free graphs with chromatic number four and arbitrarily large odd girth. As a distance-regular graph with odd