Radii of regular polytopes
| dc.creator | Brandenberg, Rene | |
| dc.date | 2003-08-13 | |
| dc.date.accessioned | 2026-07-07T05:00:22Z | |
| dc.date.available | 2026-07-07T05:00:22Z | |
| dc.description | This paper deals with the three types of regular polytopes which exist in all dimensions -- regular simplices, cubes and regular cross-polytopes -- and their outer and inner radii. While the inner radii of regular simplices are well studied, only a few cases are solved for the outer radii. We give a lower bound on these radii, and show that this bound is tight in almost 3 out of 4 dimensions. In a further section we complete the results about inner and outer radii of general boxes and cross-polytopes. Finally, because cubes and regular cross-polytopes are radii-minimal projections of simplices, we show that it is possible to deduce the results about their radii from the results about the outer radii of simplices. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308121 | |
| dc.identifier | http://arxiv.org/abs/math/0308121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68306 | |
| dc.subject | General Mathematics | |
| dc.subject | 52B12;52B11;52B60 | |
| dc.title | Radii of regular polytopes | |
| dc.type | text |