Small covers of the dodecahedron and the 120-cell

Garrison, Anne; Scott, Richard

doi:10.1090/S0002-9939-02-06577-2

Small covers of the dodecahedron and the $120$-cell
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by Anne Garrison and Richard Scott PDF

Proc. Amer. Math. Soc. 131 (2003), 963-971 Request permission

Abstract:

Let $P$ be the right-angled hyperbolic dodecahedron or $120$-cell, and let $W$ be the group generated by reflections across codimension-one faces of $P$. We prove that if $\Gamma \subset W$ is a torsion free subgroup of minimal index, then the corresponding hyperbolic manifold ${\mathbb H}^n/\Gamma$ is determined up to home omorphism by $\Gamma$ modulo symmetries of $P$.

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