hypercube

hypercube \hypercube\ n.
   A mathematical object existing in more than three dimensions,
   analogous to the cube in that each two-dimensional facet of
   the surface is a square; a generalization of a cube in more
   than three dimensions.
   [PJC]
    

hypercube

   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}.

   (1994-11-17)