Small Covers of the Dodecahedron and the 120-cell

Abstract

Let P be the right-angled dodecahedron or 120-cell in hyperbolic space, and let W be the group generated by reflections across codimension-one faces of P. We prove that if Gamma is a torsion-free subgroup of minimal index in W, then the corresponding hyperbolic manifold H^n/Gamma is determined up to homeomorphism by Gamma (modulo symmetries of P).

8 pages, abstract corrected (the result is for minimal index subgroups of W), article unchanged