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9-cube. In geometry, a 9-cube is a nine- dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces . It can be named by its Schläfli symbol {4,3 7 }, being composed of three 8-cubes around each 7-face.
In geometry, a hypercube is an n -dimensional analogue of a square ( n = 2) and a cube ( n = 3 ). 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. A unit hypercube's longest diagonal in n ...
The iPSC used a Hypercube internetwork topology of connections between the processors internally inspired by the Caltech Cosmic Cube research project. For that reason, it was configured with nodes numbering with power of two, which correspond to the corners of hypercubes of increasing dimension.
Hypercubic honeycomb. In geometry, a hypercubic honeycomb is a family of regular honeycombs ( tessellations) in n - dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group Rn (or B~n–1) for n ≥ 3 . The tessellation is constructed from 4 n - hypercubes per ridge. The vertex figure is a cross ...
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right angles .
The cross-polytope is the convex hull of its vertices. The n -dimensional cross-polytope can also be defined as the closed unit ball (or, according to some authors, its boundary) in the ℓ 1 -norm on Rn : In 1 dimension the cross-polytope is simply the line segment [−1, +1], in 2 dimensions it is a square (or diamond) with vertices { (±1, 0 ...
Uniform 9-polytope. In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets . A uniform 9-polytope is one which is vertex-transitive, and constructed from uniform 8-polytope facets .
Partial cube. In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. [1] In other words, a partial cube can be identified with a subgraph of a hypercube in such a way that the distance between any two vertices in the partial cube is the same as the distance between those vertices in the hypercube.
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