Only the simplexes away from formula 52 shrink. These are the regular simplices or simplexes. The theorem can be generalized to higher-dimensional simplexes using barycentric coordinates. Every convex polytope may be dissected into simplexes. The simplexes in a chain need not be unique; they may occur with multiplicity. "Generalized orthoplexes" have regular simplexes (real) as facets. The facets are generalized ("n"-1)-cube and the vertex figure are regular simplexes.