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
Compound of 5-cube and 5-orthoplex different edges. Compound of 5-cube and 5-orthoplex In 5-dimensional geometry, the 5-cube 5-orthoplex compound is a polytope compound composed of a regular 5-cube and dual regular 5-orthoplex. A "compound polytope" is a figure that is composed of several polytopes sharing a common center. The outer vertices of a compound can be connected to form a convex polytope called the convex hull. The compound is a facetting of the convex hull. In 5-polytope compounds constructed as dual pairs, the hypercells and vertices swap positions and cells and edges swap positions. Because of this the number of hypercells and vertices are equal,