Geodesic
Projected products of polygons
Ziegler, Günter1
1Inst. Mathematics, MA 6-2, TU Berlin, D-10623 Berlin, Germany
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 122-134

Voir la notice de l'article provenant de la source American Mathematical Society

It is an open problem to characterize the cone of $f$-vectors of $4$-dimensional convex polytopes. The question whether the “fatness” of the $f$-vector of a $4$-polytope can be arbitrarily large is a key problem in this context. Here we construct a $2$-parameter family of $4$-dimensional polytopes $\pi (P^{2r}_n)$ with extreme combinatorial structure. In this family, the “fatness” of the $f$-vector gets arbitrarily close to $9$; an analogous invariant of the flag vector, the “complexity,” gets arbitrarily close to $16$. The polytopes are obtained from suitable deformed products of even polygons by a projection to $\mathbb {R}^4$.
DOI : 10.1090/S1079-6762-04-00137-4

Ziegler, Günter  1

1 Inst. Mathematics, MA 6-2, TU Berlin, D-10623 Berlin, Germany 
Ziegler, Günter. Projected products of polygons. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 122-134. doi: 10.1090/S1079-6762-04-00137-4
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