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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 dimensions is equal to .
Hypercube graph. In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n -dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2n vertices, 2n – 1n edges, and is a regular graph with n edges touching each vertex.
The illustration shows a cube, a graph with eight vertices and twelve edges, and an induced path of length four in this graph. A straightforward case analysis shows that there can be no longer induced path in the cube, although it has an induced cycle of length six. The problem of finding the longest induced path or cycle in a hypercube, first posed by Kautz (1958), is known as the snake-in ...
Cube. (film series) Cube is a Canadian science fiction horror film series. The films were directed by Vincenzo Natali, [1] Andrzej Sekuła, [2] Ernie Barbarash [3] and Yasuhiko Shimizu respectively. The films are centered, with slight variations, on the same science-fictional setting: a gigantic, mechanized cubical structure of unknown purpose ...
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been perturbed. Klee and Minty demonstrated that George Dantzig 's simplex algorithm has poor worst-case performance when initialized at one corner of their "squashed cube". On the three-dimensional version, the simplex algorithm and the ...
Cube-connected cycles. The cube-connected cycles of order 3, arranged geometrically on the vertices of a truncated cube. In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced by Preparata & Vuillemin (1981) for use as a network topology in ...
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