Several families of incommensurable noncompact hyperbolic Coxeter polytopes

Lizi Guo; Jiming Ma; Yourong Zang; Fangting Zheng

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arXiv · 2607.14715

Several families of incommensurable noncompact hyperbolic Coxeter polytopes

Lizi Guo·Jiming Ma·Yourong Zang·Fangting Zheng

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Abstract

We classify all 141 finite-volume hyperbolic Coxeter five-dimensional polytopes with eight facets, of which 125 are noncompact. Using maximal-cusp density and a noncompact analog of Bogachev-Douba-Raimbault's argument, we construct infinitely many pairwise incommensurable noncompact Coxeter polytopes in dimensions 4, 5, 6, 7, and 9, with the number of commensurability classes growing at least exponentially in volume.

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Lizi Guo, Jiming Ma, Yourong Zang, Fangting Zheng. 2026-07-16. Several families of incommensurable noncompact hyperbolic Coxeter polytopes. https://arxiv.org/abs/2607.14715

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