Díaz Sánchez, Raquel (1997) Non-convexity of the space of dihedral angles of hyperbolic polyhedra. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 325 (9). pp. 993-998. ISSN 0764-4442
![[img]](/style/images/fileicons/application_pdf.png) | PDF Restricted to Repository staff only until 31 December 2020. 433Kb |
Official URL: http://www.sciencedirect.com/science/article/pii/S0764444297890921
Abstract
We prove that the space of dihedralangles of hyperbolic three-dimensional polyhedra, or of compact hyperbolicpolyhedra, of a given combinatorial type is not convex.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Three-dimensional polytopes; Spherical and hyperbolic convexity |
| Subjects: | Sciences > Mathematics > Geometry |
| ID Code: | 15708 |
| References: | E. Andreev. On convex polyhedra in Lobachevskii spaces. Math. USSR Sb., 10 (1970), pp. 413–440 E. Andreev. Convex polyhedra of finite volume in Lobachebskii space. Math. USSR Sb., 12 (1970), pp. 255–259 R. Diaz. Matrices de Gram y espacios de ángulos diédricos de poliedros. Ph. D. Thesis Universidad Complutense de Madrid (1996) R. Díaz. A characterization of Gram matrices of polytopes. preprint (1997) B. Grünbaum. Convex Polytopes. Pure and Applied Mathematics, Vol. XVI Interscience publishers (1967) C. Hodgson, I. Rivin. A characterization of compact convex polyhedra in hyperbolic 3-space. Invent. Math., 111 (1993), pp. 77–111 I. Rivin. On geometry of convex ideal polyhedra in hyperbolic 3-space. Topology, Vol. 32 (No. 1) (1993), pp. 87–92 I. Rivin. A characterization of ideal polyhedra in hyperbolic 3-space. Ann. Math., Vol. 143 (No. 1) (1996), pp. 51–70 |
| Deposited On: | 21 Jun 2012 10:17 |
| Last Modified: | 08 May 2013 19:30 |
Repository Staff Only: item control page
