When considering step prisms, first think about a purely n-gonal multiprism {n} x {n} x {n} x .... x {n}, say k times. That one clearly would be a polytope living within 2k dimensions and having n^k vertices. In fact, its vertices thus can be coded by all the k-tuples of (independently chosen) numb...

It's outstanding that all 4D dice with 5+ cells is possible, "gyrochora" being the general method.
Stella4D tells gyrochora are dual of step prisms, which can be created by Stella4D.
But what is a step prism? I can't find any reference to it in Google or DBpia.