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Compact hyperbolic Coxeter four-dimensional polytopes with eight facets

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Abstract

In this paper, we obtain the complete classification for compact hyperbolic Coxeter four-dimensional polytopes with eight facets.

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Data availability

The result data are completely stated in this manuscript. The example codes and all the intermediate data are available at https://github.com/GeoTopChristy/HCPdm.

Notes

  1. It is also referred to as “irreducible" in some references.

  2. Only if there is no hope to have at least 2 cases where deleted two rows and columns containing all \(d_i\) length unknowns, we compromise to find those including \(d_i-1\) length unknowns.

  3. It seems that there is a small typo in Table 5 of [23], where the lengths for \(\Sigma _2^2\) and \(\Sigma _2^3\) should be swapped.

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Acknowledgements

We would like to thank Amanda Burcroff a lot for communicating with us about her result and pointing out several confusing drawing typos in the first arXiv version. The computations are intricate and complex, and the list now is much more convincing due to the mutual check. We are also grateful to Nikolay Bogachev for his interest and discussion about the results, and noting the missing of a hyperparallel distance data and some textual mistakes in a previous version. The authors would also like to thank the referees for their valuable comments for improving the article. The computations throughout this paper are performed on a cluster of servers of PARATERA, engrid12, line priv_para (CPU:Intel(R) Xeon(R) Gold 5218 16 Core v5@2.3GHz).

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  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Jiming Ma

  2. Department of Pure Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China

    Fangting Zheng

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Jiming Ma was partially supported by NSFC 11771088 and 12171092. Fangting Zheng was supported by NSFC 12101504, Natural Science Foundation of the Jiangsu Higher Education Institutions of China 21KJB110009 and XJTLU Research Development Fund RDF-19-01-29.

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Ma, J., Zheng, F. Compact hyperbolic Coxeter four-dimensional polytopes with eight facets. J Algebr Comb 59, 225–290 (2024). https://doi.org/10.1007/s10801-023-01279-7

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