Hyperbolic manifolds and tessellations of type {3,5,3} associated with L_2(q)

Abstract

We classify the normal subgroups K of the tetrahedral group ∆ = [3, 5, 3] + , the even subgroup of the Coxeter group Γ = [3, 5, 3], with ∆/K isomorphic to a finite simple group L 2 (q). We determine their normalisers N (K) in the isometry group of hyperbolic 3-space H 3 , the isometry groups N (K)/K of the associated hyperbolic 3manifolds H 3 /K, and the symmetry groups N Γ (K)/K of the icosahedral tessellations of these manifolds, giving a detailed analysis of how L 2 (q) acts on these tessellations.