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- W4226163148 abstract "We complete the classification of compact hyperbolic Coxeter $d$-polytopes with $d+4$ facets for $d=4$ and $5$. By previous work of Felikson and Tumarkin, the only remaining dimension where new polytopes may arise is $d=6$. We derive a new method for generating the combinatorial type of these polytopes via the classification of point set order types. In dimensions $4$ and $5$, there are $348$ and $51$ polytopes, respectively, yielding many new examples for further study. We furthermore provide new upper bounds on the dimension $d$ of compact hyperbolic Coxeter polytopes with $d+k$ facets for $k leq 10$. It was shown by Vinberg in 1985 that for any $k$, we have $d leq 29$, and no better bounds have previously been published for $k geq 5$. As a consequence of our bounds, we prove that a compact hyperbolic Coxeter $29$-polytope has at least $40$ facets." @default.
- W4226163148 created "2022-05-05" @default.
- W4226163148 creator A5024470947 @default.
- W4226163148 date "2022-01-10" @default.
- W4226163148 modified "2023-09-27" @default.
- W4226163148 title "Near Classification of Compact Hyperbolic Coxeter $d$-Polytopes with $d+4$ Facets and Related Dimension Bounds" @default.
- W4226163148 doi "https://doi.org/10.48550/arxiv.2201.03437" @default.
- W4226163148 hasPublicationYear "2022" @default.
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