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
Rubik's Cube group define orientation. One choice is the following group, given by generators (the last generator is a 3 cycle on the edges): Since "C" is a normal subgroup and the intersection of "C" and "C" is the identity and their product is the whole cube group, it follows that the cube group "G" is the semi-direct product of these two groups. That is Next we can take a closer look at these two groups. The structure of "C" is since the group of rotations of each corner (resp. edge) cube is formula_30 (resp. formula_31), and in each case all but one