Abstract:An orbit polytope is the convex hull of an orbit under a finite group G GL(d, R). We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense set of generic points such that the orbit polytopes of generic points have conjugated affine symmetry groups. We prove that the symmetry group of a generic orbit polytope is again G if G is itself the affine symmetry group of some orbit polytope, or if G is absolutely irreducible. On the other hand, we d… Show more
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