The special cuts of 600-cell
Abstract
A polytope is called regular-faced if every one of its facets is a regular polytope. The 4-dimensional regular-faced polytopes were determined by G. Blind and R. Blind BlBl2,roswitha,roswitha2. The last class of such polytopes is the one which consists of polytopes obtained by removing a set of non-adjacent vertices (an independent set) of the 600-cell. These independent sets are enumerated up to isomorphism and it is determined that the number of polytopes in this last class is 314,248,344.
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