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arXiv · 2005.05746

On chiral polytopes having a group PSL(3,q) as automorphism group

Dimitri Leemans·Adrien Vandenschrick
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Abstract

For each prime power $q\geq 5$, we construct a rank four chiral polytope that has a group $PSL(3,q)$ as automorphism group and Schl\"afli type $\{q-1,\frac{2(q-1)}{(3,q-1)},q-1\}$. We also construct rank five polytopes for some values of $q$ and we show that there is no chiral polytope of rank at least six having a group $PSL(3,q)$ or $PSU(3,q)$ as automorphism group.

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Dimitri Leemans, Adrien Vandenschrick. 2020-05-12. On chiral polytopes having a group PSL(3,q) as automorphism group. https://arxiv.org/abs/2005.05746

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