A characterization of Gram matrices of polytopes
| dc.contributor.author | Díaz Sánchez, Raquel | |
| dc.date.accessioned | 2023-06-20T16:54:22Z | |
| dc.date.available | 2023-06-20T16:54:22Z | |
| dc.date.issued | 1999 | |
| dc.description.abstract | We give a characterization of the Gram matrices of spherical and finite-volume hyperbolic polytopes of a given combinatorial type. This is done in terms of the signs of certain minors of the Gram matrix. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15709 | |
| dc.identifier.doi | 10.1007/PL00009440 | |
| dc.identifier.issn | 0179-5376 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/fapge0cdq2cpq7lp/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57388 | |
| dc.issue.number | 4 | |
| dc.journal.title | Discrete and Computational Geometry | |
| dc.language.iso | eng | |
| dc.page.final | 601 | |
| dc.page.initial | 581 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 514 | |
| dc.subject.keyword | n -dimensional polytopes | |
| dc.subject.ucm | Geometría | |
| dc.subject.unesco | 1204 Geometría | |
| dc.title | A characterization of Gram matrices of polytopes | |
| dc.type | journal article | |
| dc.volume.number | 21 | |
| dcterms.references | A.D. Alexandrow, Konvexe Polyeder, Berlin: Akademie Verlag, 1958 (original in Russian: GITTL, Moscow, 1950). 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 Lobachebskii space, Math. USSR-Sb. 12 (1970), 255–259. E.M. Andreev, The intersection of the plane boundaries of a polytope with acute angles, Mat. Zametki 8 (1970), 521–527. M.M. Bayer, C.W. Lee, Combinatorial aspects of convex polytopes, in Handbook of Convex Geometry, ed. by P.M. Gruber and J.M. Wills, Amsterdam: North-Holland, 1993. J. Bokowski, B. Sturmfels, Polytopal and nonpolytopal spheres, an algorithmic approach, Israel J. Math., 57(3) (1987), 257–271. A.L. Cauchy, Sur les polygones et poly`edres, J. Ecole Polytechnique 16 (1813), 87–99. H.S.M. Coxeter, Discrete groups generated by reflections, Ann. of Math. 35(2) (1934), 588–621. R. Díaz, Matrices de Gram y espacios de ángulos diédricos de poliedros, Ph.D. Thesis, Universidad Complutense de Madrid, June 1996. B. Gr¨unbaum, Convex Polytopes, Pure and Applied Mathematics,Vol. XVI, NewYork: Interscience, 1967. H.M. Hilden, M.T. Lozano, J.M. Montesinos, W.C. Whitten, On universal groups and threemanifolds, Invent. Math. 87 (1987), 441–456. J.F.P. Hudson, Piecewise Linear Topology, New York: Benjamin, 1969. B. Iversen, Hyperbolic Geometry, Cambridge: Cambridge University Press, 1992. F. Lann´er, On complexes with transitive groups of automorphisms, Comm. Sem. Math. Univ. Lund 11 (1950), 1–71. J. Milnor, The Schl¨afli differential equality, in Collected papers, Vol 1, Houston: Publish or Perish, 1994. I. Rivin, C.D. Hodgson, A characterization of compact convex polyhedra in hyperbolic 3-space, Invent. Math. 111 (1993), 77–111. I. Rivin, On geometry of convex ideal polyhedra in hyperbolic 3-space, Topology 32(1) (1993), 87–92. I. Rivin, A characterization of ideal polyhedra in hyperbolic 3-space, Ann. of Math. 143(1) (1996), 51–70. C.P. Rourke, B.J. Sanderson, Introduction to Piecewise-Linear Topology, New York: Springer-Verlag, 1972. W. Thurston, The Geometry and Topology of 3-manifolds, Princeton University Notes, preprint. E.B. Vinberg, Hyperbolic reflection groups, Russian Math. Surveys 40(1) (1985), 31–75. E.B. Vinberg, Volumes of non-Euclidean polyhedra, Russian Math. Surveys 48(2) (1993), 15–45. E.B. Vinberg (ed.), Geometry II, New York: Springer-Verlag, 1993. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | ad6ca69d-67a0-4e6d-9177-6a5439e93ce3 | |
| relation.isAuthorOfPublication.latestForDiscovery | ad6ca69d-67a0-4e6d-9177-6a5439e93ce3 |
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