Three-Dimensional Classical Groups Acting on Polytopes

Let V be a 3-dimensional vector space over a finite field. We show that any irreducible subgroup of GL(V ) that arises as the automorphism group of an regular polytope preserves a nondegenerate symmetric bilinear form on V . In particular, the only classical groups on V that arise as automorphisms of such polytopes are the orthogonal groups.

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Peter A. Brooksbank, Deborah A. Vicinsky
• Keywords: 3-dimensional Vector Space, DCG 2010, Irreducible Subgroup, Nondegenerate Symmetric Bilinear