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In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
The Universal Classification System for Hypercubes (John R. Hendricks) requires that for any dimension hypercube, all possible lines sum correctly for the hypercube to be considered perfect magic. Because of the confusion with the term perfect , nasik is now the preferred term for any magic hypercube where all possible lines sum to S .
In geometry, a 10-cube is a ten-dimensional hypercube.It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces, 8064 5-cube 5-faces, 3360 6-cube 6-faces, 960 7-cube 7-faces, 180 8-cube 8-faces, and 20 9-cube 9-faces.
In geometry, an 8-cube is an eight-dimensional hypercube.It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells, 1120 tesseract 4-faces, 448 5-cube 5-faces, 112 6-cube 6-faces, and 16 7-cube 7-faces.
This same reasoning may be applied to hypercubes of any dimension. Simply stated; in an order m magic hypercube, if all possible lines of m cells sum to the magic constant, the hypercube is perfect. All lower dimension hypercubes contained in this hypercube will then also be perfect.
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