Face Numbers of 4-Polytopes and 3-Spheres (2002)
by
Günter M. Ziegler
| Venue: | Proceedings of the international congress of mathematicians, ICM 2002 |
| Citations: | 7 - 2 self |
BibTeX
@INPROCEEDINGS{Ziegler02facenumbers,
author = {Günter M. Ziegler},
title = {Face Numbers of 4-Polytopes and 3-Spheres},
booktitle = {Proceedings of the international congress of mathematicians, ICM 2002},
year = {2002},
pages = {625--634},
publisher = {Higher Education Press}
}
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Abstract
Steinitz (1906) gave a remarkably simple and explicit description of the set of all f-vectors f(P ) = (f0 , f1 , f2) of all 3-dimensional convex polytopes. His result also identifies the simple and the simplicial 3-dimensional polytopes as the only extreme cases. Moreover, it can be extended to strongly regular CW 2-spheres (topological objects), and further to Eulerian lattices of length 4 (combinatorial objects).
