The hypermetric cone on seven vertices
| dc.creator | Dutour, Mathieu | |
| dc.creator | Deza, Michel | |
| dc.date | 2001-08-26 | |
| dc.date | 2002-04-07 | |
| dc.date.accessioned | 2026-07-07T04:43:08Z | |
| dc.date.available | 2026-07-07T04:43:08Z | |
| dc.description | The hypermetric cone $HYP_n$ is the set of vectors $(d_{ij})_{1\leq i< j\leq n}$ satisfying the inequalities $\sum_{1\leq i<j\leq n} b_ib_jd_{ij}\leq 0 with b_i\in\Z and \sum_{i=1}^{n}b_i=1$. A Delaunay polytope of a lattice is called extremal if the only affine bijective transformations of it into a Delaunay polytope, are the homotheties; there is a correspondance between such Delaunay polytopes and extreme rays of $HYP_n$. We show that unique Delaunay polytopes of root lattice $A_1$ and $E_6$ are the only extreme Delaunay polytopes of dimension at most 6. We describe also the skeletons and adjacency properties of $HYP_7$ and of its dual. | |
| dc.description | 8 pages, 4 tables | |
| dc.identifier | https://arxiv.org/abs/math/0108177 | |
| dc.identifier | http://arxiv.org/abs/math/0108177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62083 | |
| dc.subject | Metric Geometry | |
| dc.title | The hypermetric cone on seven vertices | |
| dc.type | text |