Hypercube

A hypercube is the n-dimensional generalization of a square and a cube, built by sweeping a lower-dimensional cube one unit along a new direction perpendicular to all the others: a point becomes a line segment, a line segment becomes a square, a square becomes a cube, and a cube becomes a four-dimensional hypercube called a tesseract. An n-dimensional hypercube has 2 to the n vertices and 2n facets of dimension n minus 1, and the longest diagonal across a unit hypercube of n dimensions has length equal to the square root of n. The shape is closed, compact and convex, made up of groups of parallel edges running in each of its dimensions, each group perpendicular to every other and all edges the same length.