3-Manifolds from Platonic Solids

Details 3-Manifolds from Platonic Solids 3-Manifolds from Platonic Solids

2001-04-18

arxiv.org/abs/math/0104182v1

Topology and its Applications, 138 (2004) 253-263

Mathematics

Geometric Topology

8 pages

Scientific paper

The problem of classifying, upto isometry (or similarity), the orientable
spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the
faces of a Platonic solid is formulated in the language of Coxeter groups. In
the spherical and hyperbolic cases, this allows us to complete the
classification begun by Lorimer, Richardson and Rubinstein and Best.

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