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In its simplest form, a four-dimensional cube, which can be considered as two three-dimensional cubes connected at equivalent corners. Connecting the corners of four-dimensional cubes gives a five-dimensional hypercube. In general, an (n+1)-dimensional hypercube can be generated by connecting the corners of n-dimensional hypercubes, and has twice as many corners as the n-dimensional hypercube.

Several multiprocessing systems have an architecture based on the hypercube, where processors replace corners and communication links replace edges. In an n-dimensional hypercube network, no processor is more than n links from any other processor; doubling the number of processors by using an (n+1)-dimensional network means information has to travel over only one additional connection. However, as the number of processors increases, the number of connections each one must make has also to be increased.

Subjects: Computing.

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