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Symmetry groups of vertex-transitive polytopes

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Abstract

Groups which are not isomorphic to the symmetry group of any vertextransitive polytope (of any dimension) are characterized as generalized dicyclic, or abelian groups but not elementary 2-groups. The same class of groupsG is also characterized by the existence of a permutation groupP acting onG, containingG* (the regular representation ofG) as a proper subgroup, such that the members of the stabilizerP u of the unitu ε G take everyg ε G tog ±1.

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  1. Dept. of Algebra, Eötvös L. University, Muzeum krt. 6-8, H-1088, Budapest, Hungary

    László Babai

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  1. László Babai
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Babai, L. Symmetry groups of vertex-transitive polytopes. Geom Dedicata 6, 331–337 (1977). https://doi.org/10.1007/BF02429904

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