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
8-cube the column element. The configurations for dual polytopes can be seen by rotating the matrix elements by 180 degrees. formula_1 The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing one mirror at a time. Applying an "alternation" operation, deleting alternating vertices of the octeract, creates another uniform polytope, called a "8-demicube", (part of an infinite family called demihypercubes), which has 16 demihepteractic and 128 8-simplex facets. 8-cube In geometry, an 8-cube is an eight-dimensional hypercube (8-cube). It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells,