3-manifolds from Platonic solids

B Everitt

doi:10.1016/j.topol.2003.08.025

3-manifolds from Platonic solids

B Everitt

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The problem of classifying, up to isometry, the orientable spherical and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. This allows us to complete the classification begun by Best [Canad. J. Math. 23 (1971) 451], Lorimer [Pacific J. Math. 156 (1992) 329], Richardson and Rubinstein [Hyperbolic manifolds from a regular polyhedron, Preprint]. (C) 2003 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	253-263
Number of pages	11
Journal	Topology and its Applications
Volume	138
Issue number	1-3
DOIs	https://doi.org/10.1016/j.topol.2003.08.025
Publication status	Published - 28 Mar 2004

Keywords

3-manifolds
Coxeter groups
DISCRETE-SUBGROUPS
SPACES

Access to Document

10.1016/j.topol.2003.08.025

http://dx.doi.org/1016/j.topol.2003.08.025

Cite this

@article{808a0e5fa4fb479e968bbe2ae3cc0bb6,

title = "3-manifolds from Platonic solids",

abstract = "The problem of classifying, up to isometry, the orientable spherical and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. This allows us to complete the classification begun by Best [Canad. J. Math. 23 (1971) 451], Lorimer [Pacific J. Math. 156 (1992) 329], Richardson and Rubinstein [Hyperbolic manifolds from a regular polyhedron, Preprint]. (C) 2003 Elsevier B.V. All rights reserved.",

keywords = "3-manifolds, Coxeter groups, DISCRETE-SUBGROUPS, SPACES",

author = "B Everitt",

year = "2004",

month = mar,

day = "28",

doi = "10.1016/j.topol.2003.08.025",

language = "English",

volume = "138",

pages = "253--263",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

number = "1-3",

}

TY - JOUR

T1 - 3-manifolds from Platonic solids

AU - Everitt, B

PY - 2004/3/28

Y1 - 2004/3/28

N2 - The problem of classifying, up to isometry, the orientable spherical and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. This allows us to complete the classification begun by Best [Canad. J. Math. 23 (1971) 451], Lorimer [Pacific J. Math. 156 (1992) 329], Richardson and Rubinstein [Hyperbolic manifolds from a regular polyhedron, Preprint]. (C) 2003 Elsevier B.V. All rights reserved.

AB - The problem of classifying, up to isometry, the orientable spherical and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. This allows us to complete the classification begun by Best [Canad. J. Math. 23 (1971) 451], Lorimer [Pacific J. Math. 156 (1992) 329], Richardson and Rubinstein [Hyperbolic manifolds from a regular polyhedron, Preprint]. (C) 2003 Elsevier B.V. All rights reserved.

KW - 3-manifolds

KW - Coxeter groups

KW - DISCRETE-SUBGROUPS

KW - SPACES

U2 - 10.1016/j.topol.2003.08.025

DO - 10.1016/j.topol.2003.08.025

M3 - Article

SN - 0166-8641

VL - 138

SP - 253

EP - 263

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3

ER -