2004
DOI: 10.1016/j.topol.2003.08.025
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3-manifolds from Platonic solids

Abstract: 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 [11], Richardson and Rubinstein [17] and Best [2].

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Cited by 29 publications
(118 citation statements)
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“…Best [9]. The spherical dodecahedron spaces were discovered by H. Poincaré, P. J. Lorimer [17] and B. Everitt [16]. Table 2.…”
Section: Results In 3-dimensional Spaces Of Constant Curvaturementioning
confidence: 99%
See 2 more Smart Citations
“…Best [9]. The spherical dodecahedron spaces were discovered by H. Poincaré, P. J. Lorimer [17] and B. Everitt [16]. Table 2.…”
Section: Results In 3-dimensional Spaces Of Constant Curvaturementioning
confidence: 99%
“…In [14,15] the examination was extended also to the other homogeneous 3-spaces. The octahedron manifolds were discovered by J. M. Montesinos [8], B. Everitt [16] and M. Šarać, while the 3 icosahedron manifolds were enumerated by L. A. Best [9].…”
Section: Results In 3-dimensional Spaces Of Constant Curvaturementioning
confidence: 99%
See 1 more Smart Citation
“…Among the Platonic polyhedra it was applied in [9], [10] to the Poincare dodecahedron with H the binary icosahedral group. An algorithm due to Everitt in [7] describes homotopies for spherical 3-manifolds from five Platonic polyhedra. Following it we found and applied in [11] for the tetrahedron as H the cyclic group C 5 .…”
Section: Introductionmentioning
confidence: 99%
“…For the group action we start from the Coxeter group G < O(4, R) [8], [7] p. 254, with the diagram Fig. 1.…”
mentioning
confidence: 99%