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
Magic cube classes Perfect magic cube. Nasik; A. H. Frost (1866) referred to all but the simple magic cube as Nasik!<br> C. Planck (1905) redefined "Nasik" to mean magic hypercubes of any order or dimension in which all possible lines summed correctly.<br> i.e. Nasik is a preferred alternate, and less ambiguous term for the "perfect" class.<br>Minimum correct summations required = 13"m". All pan-"r"-agonals sum correctly for "r" = 1, 2 and 3. Alternate Perfect Note that the above is a relatively new definition of "perfect". Until about 1995 there was much confusion about what constituted a "perfect" magic cube (see the discussion under