Geodesic
Regular 4-polytopes from the livingstone graph of Janko's first group
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 193-214.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Janko group $J _{1}$ has, up to duality, exactly two regular rank four polytopes, of respective Schläfli types ${5,3,5}$ and ${5,6,5}$. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.
Keywords: keywords regular abstract polytopes, first group of janko, livingstone graph 
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     title = {Regular 4-polytopes from the livingstone graph of {Janko's} first group},
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     pages = {193--214},
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Hartley, Michael I.; Hubard, Isabel; Leemans, Dimitri. Regular 4-polytopes from the livingstone graph of Janko's first group. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 193-214. http://geodesic.mathdoc.fr/item/JAC_2012__35_2_a6/