  A polytope is called {\em 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 \cite{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 $314,248,344$.
