Geodesic
Polytopes with groups of type PGL_2(q)
Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 163-171.

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There exists a unique regular polytope of rank at least 4 whose full automorphism group is a projective general linear group PGL2(q), q a prime power. This polytope is the 4-simplex and the corresponding group is PGL2(5) = S5.
DOI : 10.26493/1855-3974.102.290
Keywords: abstract polytopes, regular polytopes, projective linear groups 
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Dimitri Leemans; Egon Schulte. Polytopes with groups of type PGL_2(q). Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 163-171. doi : 10.26493/1855-3974.102.290. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.102.290/

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