Groups of type L2(q) acting on polytopes
Abstract
We prove that if G is a string C-group of rank 4 and G is isomorphic to L2(q) with q a prime power, then q must be 11 or 19. The polytopes arising are Grunbaum's 11-cell of type 3,5,3 for L2(11) and Coxeter's 57-cell of type 5,3,5 for L2(19), each a locally projective regular 4-polytope.
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