Geodesic
Two atlases of abstract chiral polytopes for small groups
Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 371-382.

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We construct chiral abstract polytopes in two different ways. Firstly we seek them as quotients of regular polytopes arising from the Atlas of Small Regular Polytopes (http://www.abstract-polytopes.com/atlas/); the resulting atlas of chiral polytopes atlas is available on the website http://www.abstract-polytopes.com/chiral/. Secondly, for each almost simple group Γ such that S ≤ Γ ≤ Aut(S) where S is a simple group and Γ is a group of order less than 900,000 listed in the Atlas of Finite Groups, we give, up to isomorphism, the number of abstract chiral polytopes on which Γ acts regularly. The results have been obtained using a series of Magma programs. All these polytopes are made available on the third author's website, at http://math.auckland.ac.nz/~dleemans/CHIRAL/.
DOI : 10.26493/1855-3974.204.f8b
Keywords: abstract chiral polytopes, almost simple groups 
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Michael Ian Hartley; Isabel Hubard; Dimitri Leemans. Two atlases of abstract chiral polytopes for small groups. Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 371-382. doi : 10.26493/1855-3974.204.f8b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.204.f8b/

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