Each row of Pascal's triangle gives the number of vertices at each distance from a fixed vertex in an "n"-dimensional cube. For example, in three dimensions, the third row (1 3 3 1) corresponds to the usual three-dimensional cube: fixing a vertex "V", there is one vertex at distance 0 from "V" (that is, "V" itself), three vertices at distance 1, three vertices at distance and one vertex at distance (the vertex opposite "V"). The second row corresponds to a square, while larger-numbered rows correspond to hypercubes in each dimension.