7-cube 7-cube In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces. It can be named by its Schläfli symbol {4,3}, being composed of 3 6-cubes around each 5-face. It can be called a hepteract, a portmanteau of tesseract (the "4-cube") and "hepta" for seven (dimensions) in Greek. It can also be called a regular tetradeca-7-tope or tetradecaexon, being a 7 dimensional polytope constructed from 14 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual
Multimagic cube Multimagic cube In mathematics, a "P"-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their "k"-th power for 1 ≤ "k" ≤ "P". Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic. A "P"-multimagic cube is said to be semi-perfect if the "k"-th power cubes are perfect for 1 ≤ "k" < "P", and the "P"-th power cube is semiperfect. If all "P" of the power cubes are perfect, the multimagic cube is said to be perfect. The first known