An extremum property characterizing the n-dimensional regular cross-polytope
| dc.creator | Kuperberg, Wlodzimierz | |
| dc.date | 2001-12-28 | |
| dc.date.accessioned | 2026-07-07T04:45:33Z | |
| dc.date.available | 2026-07-07T04:45:33Z | |
| dc.description | In the spirit of the Genetics of the Regular Figures, by L. Fejes Tóth, we prove the following theorem: If $2n$ points are selected in the $n$-dimensional Euclidean ball $B^n$ so that the smallest distance between any two of them is as large as possible, then the points are the vertices of an inscribed regular cross-polytope. This generalizes a result of R. A. Rankin for $2n$ points on the surface of the ball. We also generalize, in the same manner, a theorem of Davenport and Hajós on a set of $n+2$ points. As a corollary, we obtain a solution to the problem of packing $k$ unit $n$-dimensional balls $(n+2\le k\le 2n)$ into a spherical container of minimum radius. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112290 | |
| dc.identifier | http://arxiv.org/abs/math/0112290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62992 | |
| dc.subject | Metric Geometry | |
| dc.title | An extremum property characterizing the n-dimensional regular cross-polytope | |
| dc.type | text |