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hypercube    
超立方体; 超正方体

超立方体; 超正方体

hypercube
超立方体结构

hypercube
超立方

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]

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 N1 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)


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  • Hypercube - Wikipedia
    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
  • Hypercube -- from Wolfram MathWorld
    The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope It is a regular polytope with mutually perpendicular sides, and is therefore an orthotope
  • Hypercubes - Math is Fun
    In Geometry we can have different dimensions The general idea of a cube in any dimension is called a hypercube, or n-cube
  • Tesseract | Brilliant Math Science Wiki
    A tesseract, also known as a hypercube, is a four-dimensional cube, or, alternately, it is the extension of the idea of a square to a four-dimensional space in the same way that a cube is the extension of the idea of a square to a three-dimensional space
  • What Is a Tesseract or Hypercube? - Science Notes and Projects
    A tesseract or hypercube is the four-dimensional equivalent to a cube, much like a cube is a three-dimensional equivalent to a square While a cube has six square faces, a tesseract consists of eight cells
  • Hypercube - Polytope Wiki
    A hypercube is the simplest center-symmetric polytope in each respective dimension, by facet count Hypercubes are a direct generalization of squares and cubes to higher dimensions
  • Hypercube - Art of Problem Solving
    As used in geometry, a hypercube is an extrapolation of the cube or square to n dimensions When n is not specified, it's generally assumed to be 4 For example, a 4th dimensional hypercube is called a tesseract Therefore, an n-dimensional hypercube is also known as an n-cube It is best drawn and represented in non-Euclidean geometry Tesseract
  • Welcome - Hypercubing
    Hypercubing is the hobby of solving twisty puzzles (such as the Rubik’s cube) in higher dimensions The ways that twisty puzzles move are mathematically well defined, and can be generalized to higher spatial dimensions These puzzles can then be visualized and simulated using computer software
  • Understanding Hypercubes
    Let every node in the hypercube communicate with its immediate neighbor, that is, another node with an address identical to itself except one bit is flipped, and let the bit which is flipped be the same for all nodes
  • Tesseract - Wikipedia
    The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope The Oxford English Dictionary traces the word tesseract to Charles Howard Hinton 's 1888 book A New Era of Thought





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