Groups of type L2(q) acting on polytopes

Dimitri Leemans 1 , 1  and Egon Schulte 2 , 2
  • 1 Université Libre de Bruxelles, Département de Mathématiques - C.P.216, Boulevard du Triomphe, B-1050 Bruxelles.
  • 2 Northeastern University, Department of Mathematics, 360 Huntington Avenue, Boston, MA 02115, USA.

Abstract

We prove that if G is a string C-group of rank 4 and GL2(q) with q a prime power, then q must be 11 or 19. The polytopes arising are Grünbaum'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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Advances in Geometry is a mathematical journal which publishes original research articles of excellent quality in the area of geometry. Geometry is a field of long-standing tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity, and geometric ideas and the geometric language permeate all of mathematics.

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