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On Regular Polytopes of 2-Power Order

  • Branko Grünbaum Memorial Issue
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Abstract

For each \(d\ge 3\), \(n \ge 5\), and \(k_1, k_2, \ldots , k_{d-1}\ge 2\) with \(k_1+k_2+\cdots +k_{d-1}\le n-1\), we show how to construct a regular d-polytope whose automorphism group is of order \(2^n\) and whose Schläfli type is \(\{2^{k_1},2^{k_2}, \ldots , 2^{k_{d-1}}\}\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11571035, 11731002) and the 111 Project of China (B16002). The authors thank two anonymous referees whose comments and suggestions improved this paper.

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Correspondence to Dimitri Leemans.

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Hou, DD., Feng, YQ. & Leemans, D. On Regular Polytopes of 2-Power Order. Discrete Comput Geom 64, 339–346 (2020). https://doi.org/10.1007/s00454-019-00119-5

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  • DOI: https://doi.org/10.1007/s00454-019-00119-5

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