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
Soma cube their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, and six combinations of four cubes that satisfy this condition, of which two are mirror images of each other (see Chirality). Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube. The Soma cube was analyzed in detail by John Horton Conway on September 1958 in Mathematical Games column in "Scientific American", and the book "Winning Ways for your Mathematical Plays" also contains a detailed analysis of the Soma