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Journal Articles Journal of the London Mathematical Society Year : 2022

Deformation spaces of Coxeter truncation polytopes

Abstract

A convex polytope P in the real projective space with reflections in the facets of P is a Coxeter polytope if the reflections generate a subgroup Γ of the group of projective transformations so that the Γ-translates of the interior of P are mutually disjoint. It follows from work of Vinberg that if P is a Coxeter polytope, then the interior Ω of the Γ-orbit of P is convex and Γ acts properly discontinuously on Ω. A Coxeter polytope P is 2-perfect if P ∖ Ω consists of only some vertices of P. In this paper, we describe the deformation spaces of 2-perfect Coxeter polytopes P of dimension d ⩾ 4 with the same dihedral angles when the underlying polytope of P is a truncation polytope, i.e. a polytope obtained from a simplex by successively truncating vertices. The deformation spaces of Coxeter truncation polytopes of dimension d = 2 and d = 3 were studied respectively by Goldman and the third author.
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Dates and versions

hal-03326703 , version 1 (26-08-2021)
hal-03326703 , version 2 (15-07-2022)

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Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis. Deformation spaces of Coxeter truncation polytopes. Journal of the London Mathematical Society, 2022, ⟨10.1112/jlms.12675⟩. ⟨hal-03326703v2⟩
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