Quotient polytopes of cyclic polytopes part II: Stability of the f-vector and of the k-skeleton

This paper is the continuation of an earlier paper on quotient polytopes C(v, 2m)/F of cyclic polytopes and the associated quotient complexes C(V, 2 m)/J. Here, we study mainly what changes in the face J do not affect the f-vector of the quotient C(V, 2 m)/J. In the last section we examine the corresponding question for k-skeleta, i.e., what changes in J do not affect the isomorphism type of skel _k C(V, 2 m)/J.