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Non-rational configurations, polytopes, and surfaces
Günter M. Ziegler
It is an amazing and a bit counter-intuitive discovery by Micha Perles from the sixties that there are ``non-rational polytopes'': combinatorial types of convex polytopes that cann…
Construction and Analysis of Projected Deformed Products
Raman Sanyal, Günter M. Ziegler
We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for th…
Zonotopes With Large 2D Cuts
Thilo Rörig, Nikolaus Witte, Günter M. Ziegler
There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has Ω(n^{d-1}) vertices. For d=3 this was known, with examples provided by the "Ukrainian e…
On Kalai's conjectures concerning centrally symmetric polytopes
Raman Sanyal, Axel Werner, Günter M. Ziegler
In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture, A, became known a…
Combinatorial Stokes formulas via minimal resolutions
Bernhard Hanke, Raman Sanyal, Carsten Schultz +1
We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induce…
A Small Polyhedral Z-Acyclic 2-Complex in R4
Frank H. Lutz, Günter M. Ziegler
We present a small 4-dimensional polyhedral realization of a 2-dimensional Z-acyclic but non-contractible simplicial complex.