JP Journal of Geometry and Topology
Volume 10, Issue 3, Pages 183 - 189
(November 2010)
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A SYMMETRY EXTENSION OF STEINITZ’S LEMMA ON POLYHEDRA
M. Rostami
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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 group
then the
configuration space
of P,
with respect to symmetry group
is also a
manifold with certain dimension.