Hyperideal polyhedra in hyperbolic 3-space

Xiliang Bao; Francis Bonahon

Bulletin de la Société Mathématique de France (2002)

  • Volume: 130, Issue: 3, page 457-491
  • ISSN: 0037-9484

Abstract

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A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic 3 -space ℍ 3 which, in the projective model for ℍ 3 ⊂ ℝℙ 3 , is just the intersection of ℍ 3 with a projective polyhedron whose vertices are all outside ℍ 3 and whose edges all meet ℍ 3 . We classify hyperideal polyhedra, up to isometries of ℍ 3 , in terms of their combinatorial type and of their dihedral angles.

How to cite

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Bao, Xiliang, and Bonahon, Francis. "Hyperideal polyhedra in hyperbolic 3-space." Bulletin de la Société Mathématique de France 130.3 (2002): 457-491. <http://eudml.org/doc/272331>.

@article{Bao2002,
abstract = {A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic $3$-space $\mathbb \{H\}^3$ which, in the projective model for $\mathbb \{H\}^3\subset \mathbb \{RP\}^3$, is just the intersection of $\mathbb \{H\}^3$ with a projective polyhedron whose vertices are all outside $\mathbb \{H\}^3$ and whose edges all meet $\mathbb \{H\}^3$. We classify hyperideal polyhedra, up to isometries of $\mathbb \{H\}^3$, in terms of their combinatorial type and of their dihedral angles.},
author = {Bao, Xiliang, Bonahon, Francis},
journal = {Bulletin de la Société Mathématique de France},
keywords = {hyperbolic space; polyhedron; ideal polyhedron; hyperideal},
language = {eng},
number = {3},
pages = {457-491},
publisher = {Société mathématique de France},
title = {Hyperideal polyhedra in hyperbolic 3-space},
url = {http://eudml.org/doc/272331},
volume = {130},
year = {2002},
}

TY - JOUR
AU - Bao, Xiliang
AU - Bonahon, Francis
TI - Hyperideal polyhedra in hyperbolic 3-space
JO - Bulletin de la Société Mathématique de France
PY - 2002
PB - Société mathématique de France
VL - 130
IS - 3
SP - 457
EP - 491
AB - A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic $3$-space $\mathbb {H}^3$ which, in the projective model for $\mathbb {H}^3\subset \mathbb {RP}^3$, is just the intersection of $\mathbb {H}^3$ with a projective polyhedron whose vertices are all outside $\mathbb {H}^3$ and whose edges all meet $\mathbb {H}^3$. We classify hyperideal polyhedra, up to isometries of $\mathbb {H}^3$, in terms of their combinatorial type and of their dihedral angles.
LA - eng
KW - hyperbolic space; polyhedron; ideal polyhedron; hyperideal
UR - http://eudml.org/doc/272331
ER -

References

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