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 partial cube labeling. The isometric dimension of a partial cube is the minimum dimension of a hypercube onto which it may be isometrically embedded, and is equal to the number of equivalence classes of the Djoković–Winkler relation. For instance, the isometric dimension of an formula_9-vertex tree is its number of edges, formula_13. An embedding of a partial cube onto a hypercube of this dimension is unique, up to symmetries of the hypercube. Every hypercube and therefore every partial cube may be embedded isometrically into an integer lattice, and the lattice dimension of the partial cube is the minimum dimension of