Upper bounds for edge-antipodal and subequilateral polytopes
| dc.creator | Swanepoel, Konrad J | |
| dc.date | 2006-01-26 | |
| dc.date.accessioned | 2026-07-07T07:48:46Z | |
| dc.date.available | 2026-07-07T07:48:46Z | |
| dc.description | A polytope in a finite-dimensional normed space is subequilateral if the length in the norm of each of its edges equals its diameter. Subequilateral polytopes occur in the study of two unrelated subjects: surface energy minimizing cones and edge-antipodal polytopes. We show that the number of vertices of a subequilateral polytope in any d-dimensional normed space is bounded above by (d/2+1)^d for any d >= 2. The same upper bound then follows for the number of vertices of the edge-antipodal polytopes introduced by I.Talata (Period. Math. Hungar. 38 (1999), 231--246). This is a constructive improvement to the result of A.Pór (to appear) that for each dimension d there exists an upper bound f(d) for the number of vertices of an edge-antipodal d-polytopes. We also show that in d-dimensional Euclidean space the only subequilateral polytopes are equilateral simplices. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601638 | |
| dc.identifier | http://arxiv.org/abs/math/0601638 | |
| dc.identifier | Periodica Mathematica Hungarica 54 (2007), 99--106. | |
| dc.identifier | doi:10.1007/s-10998-007-1099-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124612 | |
| dc.subject | Metric Geometry | |
| dc.subject | 52B12; 52B05 | |
| dc.title | Upper bounds for edge-antipodal and subequilateral polytopes | |
| dc.type | text |