# The special cuts of 600-cell - Mathematics > Metric Geometry

Abstract: A polytope is called {\em regular-faced} if every one of its facets is aregular polytope. The 4-dimensional regular-faced polytopes were determined byG. Blind and R. Blind \cite{BlBl2,roswitha,roswitha2}. The last class of suchpolytopes is the one which consists of polytopes obtained by removing a set ofnon-adjacent vertices an independent set of the 600-cell. These independentsets are enumerated up to isomorphism and it is determined that the number ofpolytopes in this last class is $314,248,344$.

Author: Mathieu Dutour Sikirić, Wendy Myrvold

Source: https://arxiv.org/