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 Hn/Gamma is determined up to homeomorphism by Gamma (modulo symmetries of P).
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