  We prove that if G is a string C-group of rank 4 and G is isomorphic to
L_2(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 L_2(11) and Coxeter's 57-cell of type
{5,3,5} for L_2(19), each a locally projective regular 4-polytope.
