Article révisé par les pairs
Résumé : Our paper deals with the classification of abstract regular polytopes for almost simple groups with socle PSL(2, q). We consider all almost simple groups PSL(2, q). ≤. G≤. PΓL(2, q) and determine the maximal rank of string C-group representations for G, i.e. the maximal rank of an abstract regular polytope with automorphism group G, as well as the existence of string C-group representations of lower ranks. Similar results have already been obtained by various authors in the cases G≅. PSL(2, q) and G≅. PGL(2, q) and they are summarized in this paper.