An n-dimensional cube. Geometrically, in the vector space Rn take all the points with all coordinates between 0 and 1. Or just think of it combinatorically: call the set of n-tuples of 0s and 1s vertices; call each pair of vertices which disagrees on one coordinate only an edge; do the same for (2-dimensional) faces, and then 3-faces and so on up to the entire n-cube. Obviously, you can identify the combinatoric structure with the corresponding subsets of the cube in Rn.

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