the "birectified 5-simplex", 0, is second in a dimensional series of uniform polytopes, expressed by coxeter as k series. the "birectified 5-simplex" is the vertex figure for the third, the 1. the fourth figure is a euclidean honeycomb, 2, and the final is a noncompact hyperbolic honeycomb, 3. each progressive uniform polytope is constructed from the previous as its vertex figure.