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Chiral polyhedra and projective lines

David Elliott, Dimitri Leemans, Eugenia O’Reilly-Regueiro


In this paper we give a new proof that that there are no chiral polyhedra whose automorphism group is isomorphic to PSL(2; q) or PGL(2; q). Our proof uses the sharp 3-transitive action of PGL(2; q) on the projective line PG(1; q).


Abstract chiral polytope, polyhedron, projective linear group.

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