Hyperideal polyhedra in hyperbolic 3-space  [ Polyèdres hyperidéaux de l’espace hyperbolique de dimension 3 ]
Bulletin de la Société Mathématique de France, Tome 130 (2002) no. 3, p. 457-491
Un polyèdre hyperidéal est un polyèdre non-compact de l’espace hyperbolique 3 de dimension 3 qui, dans le modèle projectif pour 3 ℝℙ 3 , est simplement l’intersection de 3 avec un polyèdre projectif dont les sommets sont tous en dehors de 3 et dont toutes les arêtes rencontrent 3 . Nous classifions ces polyèdres hyperidéaux, à isométrie de 3 près, en fonction de leur type combinatoire et de leurs angles diédraux.
A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic 3-space 3 which, in the projective model for 3 ℝℙ 3 , is just the intersection of 3 with a projective polyhedron whose vertices are all outside 3 and whose edges all meet 3 . We classify hyperideal polyhedra, up to isometries of 3 , in terms of their combinatorial type and of their dihedral angles.
DOI : https://doi.org/10.24033/bsmf.2426
Classification:  51M09
Mots clés: espace hyperbolique, polyèdre, polyèdre idéal, hyperidéal
@article{BSMF_2002__130_3_457_0,
     author = {Bao, Xiliang and Bonahon, Francis},
     title = {Hyperideal polyhedra in hyperbolic 3-space},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {130},
     number = {3},
     year = {2002},
     pages = {457-491},
     doi = {10.24033/bsmf.2426},
     zbl = {1033.52009},
     mrnumber = {1943885},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2002__130_3_457_0}
}
Bao, Xiliang; Bonahon, Francis. Hyperideal polyhedra in hyperbolic 3-space. Bulletin de la Société Mathématique de France, Tome 130 (2002) no. 3, pp. 457-491. doi : 10.24033/bsmf.2426. http://www.numdam.org/item/BSMF_2002__130_3_457_0/

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