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- W4385292188 abstract "We construct four infinite families of chiral $3$-polytopes of type ${4, 8}$, with $1024m^4$, $2048m^4$, $4096m^4$ and $8192m^4$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are solvable groups, and when $m$ is a power of $2$, they provide examples with automorphism groups of order $2^n$ where $n geq 10$. (On the other hand, no chiral polytopes of type ${4, 8}$ exist for $n leq 9$.) In particular, our families give a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, {em Period. Math. Hungar.} 53 (2006), 231-255] and a problem proposed by Pellicer in [Developments and open problems on chiral polytopes, {em Ars Math. Contemp} 5 (2012), 333-354]." @default.
- W4385292188 created "2023-07-27" @default.
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- W4385292188 date "2023-07-22" @default.
- W4385292188 modified "2023-09-25" @default.
- W4385292188 title "Four infinite families of chiral $3$-polytopes of type ${4, 8}$ with solvable automorphism groups" @default.
- W4385292188 doi "https://doi.org/10.48550/arxiv.2307.12999" @default.
- W4385292188 hasPublicationYear "2023" @default.
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