2019/07/23 by Alexandru Chirvăsitu, Chirvasitu, Alexandru, Frieder Ladisch +3
Engineering · Mathematics · #52B11 #52B15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Metric Geometry (math.MG) #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1907.10022
openalex publication_date 2019/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study properties of the realizations of groups as the combinatorial automorphism group of a convex polytope. We show that for any non-abelian group G with a central involution there is a centrally symmetric polytope with G as its combinatorial automorphisms. We show that for each integer n, there are groups that cannot be realized as the combinatorial automorphisms of convex polytopes of dimension at most n. We also give an optimal lower bound for the dimension of the realization of a group as the group of isometries that preserves a convex polytope.