Abstract: The family of all
convex 3-polytopes in Euclidean space may be
partitioned into face-types or configuration spaces by isomorphisms of face
lattices. The configuration space of any such
3-polytope P may be subdivided further
into symmetry types by
equivalence of actions of symmetry groups on face lattices. With respect to its
natural topology on each is
manifold. In this paper, we prove that if P
is a convex 3-polytope with symmetry groupthen the
configuration space of P,
with respect to symmetry groupis also a
manifold with certain dimension.
