third integer being a specific type of figurate number corresponding to an n-cube with a number of dimensions corresponding to the exponential. For example, the exponent 2 will yield a square number or "perfect square", which can be arranged into a square shape with a side length corresponding to that of the base. Similarly, the exponent 3 will yield a perfect cube, an integer which can be arranged into a cube shape with a side length of the base. As a result, the act of raising a number to 2 or 3 is more commonly referred to as "squaring" and "cubing", respectively. However, the names of higher-order hypercubes do not appear to be in common use for higher powers. See also Hypercube interconnection network of computer architecture Hyperoctahedral group, the symmetry group of the hypercube Hypersphere Simplex Parallelotope Crucifixion (Corpus Hypercubus) (famous artwork) Notes References p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n dimensions (n ≥ 5) Cf Chapter 7.1 "Cubical Representation of Boolean Functions" wherein the notion of "hypercube" is introduced as a means of demonstrating a distance-1 code (Gray code) as the vertices of a hypercube, and then the hypercube with its vertices so labelled is squashed into two dimensions to form either a Veitch diagram or Karnaugh map. External links www.4d-screen.de (Rotation of 4D – 7D-Cube) Rotating a Hypercube by Enrique Zeleny, Wolfram Demonstrations Project. Stereoscopic Animated Hypercube Rudy Rucker and Farideh Dormishian's Hypercube Downloads A001787 Number of edges in an n-dimensional hypercube. at OEIS Multi-dimensional geometry Cubes