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
Partial cube "Hamming labeling"; it represents an isometric embedding of the partial cube into a hypercube. was the first to study isometric embeddings of graphs into hypercubes. The graphs that admit such embeddings were characterized by and , and were later named partial cubes. A separate line of research on the same structures, in the terminology of families of sets rather than of hypercube labelings of graphs, was followed by and , among others. Every tree is a partial cube. For, suppose that a tree "T" has "m" edges, and number these edges (arbitrarily) from 0 to "m" − 1. Choose a