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All polytopes are coset geometries: characterizing automorphism groups of k-orbit abstract polytopes | | Isabel Hubard
; Elías Mochán
; | | Date: |
1 Aug 2022 | | Abstract: | Abstract polytopes generalize the classical notion of convex polytopes to
more general combinatorial structures. The most studied ones are regular and
chiral polytopes, as it is well-know they can be constructed as coset
geometries from their automorphism groups. This is also known to be true for 2-
and 3- orbit 3-polytopes. In this paper we show that every abstract
$n$-polytope can be constructed as a coset geometry. This construction is done
by giving a characterization, in terms of generators, relations and
intersection conditions, of the automorphism group of a $k$-orbit polytope with
given symmetry type graph. Furthermore, we use these results to show that for
all $k
eq 2$, there exist $k$-orbit $n$-polytopes with Boolean groups
(elementary abelian 2-groups) as automorphism group, for all $ngeq 3$. | | Source: | arXiv, 2208.00547 | | Services: | Forum | Review | PDF | Favorites | |
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