A generalization of Andreev's theorem
| dc.contributor.author | Díaz Sánchez, Raquel | |
| dc.date.accessioned | 2023-06-20T09:36:37Z | |
| dc.date.available | 2023-06-20T09:36:37Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | Andreev's Theorem studies the existence of compact hyperbolic polyhedra of a given combinatorial type and given dihedral angles, all of them acute. In this paper we consider the same problem but without any restriction on the dihedral angles. We solve it for the descendants of the tetrahedron, i.e. those polyhedra that can be obtained from the tetrahedron by successively truncating vertices; for instance, the first of them is the triangular prism. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15714 | |
| dc.identifier.doi | 10.2969/jmsj/1149166778 | |
| dc.identifier.issn | 0025-5645 | |
| dc.identifier.officialurl | http://projecteuclid.org/euclid.jmsj/1149166778 | |
| dc.identifier.relatedurl | http://projecteuclid.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50025 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of the mathematical society of japan | |
| dc.language.iso | eng | |
| dc.page.final | 349 | |
| dc.page.initial | 333 | |
| dc.publisher | Math Soc Japan | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 514 | |
| dc.subject.keyword | hyperbolic polyhedra | |
| dc.subject.keyword | dihedral angles | |
| dc.subject.keyword | Andreev's Theorem | |
| dc.subject.ucm | Geometría | |
| dc.subject.unesco | 1204 Geometría | |
| dc.title | A generalization of Andreev's theorem | |
| dc.type | journal article | |
| dc.volume.number | 58 | |
| dcterms.references | E. M. Andreev, On convex polyhedra in Lobachevskii spaces, Math. USSR Sb., 10 (1970), 413–440. E. M. Andreev, Convex polyhedra of finite volume in Lobachevskii space, Math. USSR Sb., 12 (1970), 255–259. R. Benedetti and J. J. Risler, Real Algebraic and Semialgebraic Geometry, Actualités Math., Hermann, 1990. A. L. Cauchy, Sur les polygones et polyèdres, J. Ec. Polytechnique, 16 (1813), 87–99. R. Díaz, Non-convexity of the space of dihedral angles of hyperbolic polyhedra, C. R. Acad. Sci. Paris Série I, 325 (1997), 993–998. R. Díaz, A Characterization of Gram Matrices of Polytopes, Discrete Comput. Geom., 21 (1999), 581–601. F. R. Gantmacher, The theory of matrices, Vol.,I, Chelsea Publishing Company, New York, 1959. B. Iversen, Hyperbolic Geometry, Cambridge Univ. Press, 1992. J. Milnor, The Schläfli differential equality, In: Collected papers Vol.,1: Geometry, Houston, Publish or Perish Inc., 1994. I. Rivin and C. D. Hodgson, A characterization of compact convex polyhedra in hyperbolic 3-space, Invent. Math., 111 (1993), 77–111. E. B. Vinberg, Hyperbolic reflection groups, Russian Math. Surveys, 40 (1985), no.,1, p.,31–75. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | ad6ca69d-67a0-4e6d-9177-6a5439e93ce3 | |
| relation.isAuthorOfPublication.latestForDiscovery | ad6ca69d-67a0-4e6d-9177-6a5439e93ce3 |
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