*Wissenschaftliches Programm* † *Liste der Vortragenden*

Sektion 12
Freitag, 22.09.2000, 14.00–14.20 Uhr, WIL A 124

Four-Polytopes with Interesting Flag-Vectors

GŁnter M. Ziegler, TU Berlin

We introduce two parameters, the “fatness” and the “complexity” of a 4-dimensional polytope, both to be computed in terms of the flag vector. It is not clear whether these parameters are at all bounded, but we provide constructions and examples of polytopes that are “fatter” and “more complex” than the examples known up to now.

Our examples disprove conjectured flag-vector inequalies by Bayer and by Billera and Ehrenborg, and they include the first infinite family of 4-polytopes that are both 2-simple and 2-simplicial.