 In a 4-dimensional polytope (or 3-dimensional cubic honeycomb) the fundamental region is bounded by four mirrors.A mirror in 4-space is a three-dimensional hyperplane, but it is more convenient for our purposes to consider only its two-dimensional intersection with the three-dimensional surface of the hypersphere; thus the mirrors form an irregular tetrahedron.Each of the sixteen regular 4-polytopes is generated by one of four symmetry groups, as follows