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(maths) a figure in a space of four or more dimensions having all its sides equal and all its angles right angles
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Examples from the Web for hypercube
Historical Examples
  • Counting the number of cubes that compose the hypercube we find that there are eight.

    The Mystery of Space Robert T. Browne
  • The hypercube or tesseract is described by moving the generating cube in the direction in which the fourth dimension extends.

    The Mystery of Space Robert T. Browne
hypercube in Science
An object resembling a three dimensional cube but having an arbitrary number of dimensions (typically more than three, although cubes and squares can be considered hypercubes in three and two dimensions). Each corner or node of a hypercube is equidistant from every other. The number of corners in a hypercube is equal to 2n, where n is the number of dimensions. Diagrams and models of hypercubes of four or more dimensions are not real hypercubes any more than a diagram of a cube is an actual cube, but they do depict the manner in which the corner points are connected. See also tesseract.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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hypercube in Technology

A cube of more than three dimensions. A single (2^0 = 1) point (or "node") can be considered as a zero dimensional cube, two (2^1) nodes joined by a line (or "edge") are a one dimensional cube, four (2^2) nodes arranged in a square are a two dimensional cube and eight (2^3) nodes are an ordinary three dimensional cube. Continuing this geometric progression, the first hypercube has 2^4 = 16 nodes and is a four dimensional shape (a "four-cube") and an N dimensional cube has 2^N nodes (an "N-cube"). To make an N+1 dimensional cube, take two N dimensional cubes and join each node on one cube to the corresponding node on the other. A four-cube can be visualised as a three-cube with a smaller three-cube centred inside it with edges radiating diagonally out (in the fourth dimension) from each node on the inner cube to the corresponding node on the outer cube.
Each node in an N dimensional cube is directly connected to N other nodes. We can identify each node by a set of N Cartesian coordinates where each coordinate is either zero or one. Two node will be directly connected if they differ in only one coordinate.
The simple, regular geometrical structure and the close relationship between the coordinate system and binary numbers make the hypercube an appropriate topology for a parallel computer interconnection network. The fact that the number of directly connected, "nearest neighbour", nodes increases with the total size of the network is also highly desirable for a parallel computer.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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