Prescribing symmetries and automorphisms for polytopes

We study finite groups that occur as combinatorial automorphism or geometric symmetry of convex polytopes. When $\Gamma$ is a subgroup the group $d$-polytope, $d\geq 3$, then there exists $d$-polytope related to original polytope with exactly $\Gamma$. both and These symmetry-breaking results are applied show for every abelian even order involution $\sigma$ $\Gamma$, centrally symmetric such corresponds central symmetry.