Cube the hypercube graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid. An extension is the three dimensional "k"-ary Hamming graph, which for "k" = 2 is the cube graph. Graphs of this sort occur in the theory of parallel processing in computers. Miscellaneous cubes Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube
Compound of 5-cube and 5-orthoplex cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa. It can be seen as the 5-dimensional analogue of a compound of cube and octahedron. The 42 Cartesian coordinates of the vertices of the compound are. The convex hull of the vertices makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound can be seen in projection as the union of the two polytope graphs. The convex hulll as the dual of the rectified 5-orthoplex will have the same vertices, but