6-cube regular 6-cube or 6-orthoplex. 6-cube In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces. It has Schläfli symbol {4,3}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the "4-cube") with "hex" for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual of a 6-cube can
Bhargava cube the edges of the corresponding faces. The integer binary quadratic form associated with this pair of faces is defined as The quadratic form is also defined as However, the former definition will be assumed in the sequel. Let the cube be formed by the integers "a", "b", "c", "d", "e", "f", "g", "h". The pairs of matrices associated with opposite edges are denoted by ("M", "N"), ("M", "N"), and ("M", "N"). The first rows of "M", "M" and "M" are respectively ["a" "b"], ["a" "c"] and ["a" "e"]. The opposite edges in the same face are the second rows. The