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ISSN 1079-6762
Projected products of polygons
Author:
Günter M. Ziegler
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 122-134
MSC (2000):
Primary 52B05; Secondary 52B11, 52B12
DOI:
https://doi.org/10.1090/S1079-6762-04-00137-4
Published electronically:
December 1, 2004
MathSciNet review:
2119033
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 $\mathbb {R}^4$.
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Additional Information
Günter M. Ziegler
Affiliation:
Inst. Mathematics, MA 6-2, TU Berlin, D-10623 Berlin, Germany
Email:
ziegler@math.tu-berlin.de
Keywords:
Discrete geometry,
convex polytopes,
$f$-vectors,
deformed products of polygons
Received by editor(s):
July 4, 2004
Published electronically:
December 1, 2004
Additional Notes:
Partially supported by Deutsche Forschungs-Gemeinschaft (DFG), via the Matheon Research Center “Mathematics for Key Technologies” (FZT86), the Research Group “Algorithms, Structure, Randomness” (Project ZI 475/3), and a Leibniz grant (ZI 475/4)
Communicated by:
Sergey Fomin
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.