Convex Polytopes: Extremal Constructions and f-Vector Shapes
| dc.creator | Ziegler, Günter M. | |
| dc.date | 2004-11-18 | |
| dc.date | 2005-12-07 | |
| dc.date.accessioned | 2026-07-07T06:39:01Z | |
| dc.date.available | 2026-07-07T06:39:01Z | |
| dc.description | These lecture notes treat some current aspects of two closely interrelated topics from the theory of convex polytopes: the shapes of f-vectors, and extremal constructions. The first lecture treats 3-dimensional polytopes; it includes a complete proof of the Koebe--Andreev--Thurston theorem, using the variational principle by Bobenko & Springborn (2004). In Lecture 2 we look at f-vector shapes of very high-dimensional polytopes. The third lecture explains a surprisingly simple construction for 2-simple 2-simplicial 4-polytopes, which have symmetric f-vectors. Lecture 4 sketches the geometry of the cone of f-vectors for 4-polytopes, and thus identifies the existence/construction of 4-polytopes of high ``fatness'' as a key problem. In this direction, the last lecture presents a very recent construction of ``projected products of polygons,'' whose fatness reaches 9-\eps. | |
| dc.description | 73 pages, large file. Lecture Notes for PCMI Summer Course, Park City, Utah, 2004; revised and slightly updated final version, December 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0411400 | |
| dc.identifier | http://arxiv.org/abs/math/0411400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100943 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 52-01, 52-02; 52B05, 52B11, 52B12 | |
| dc.title | Convex Polytopes: Extremal Constructions and f-Vector Shapes | |
| dc.type | text |