Zonotopes With Large 2D Cuts

Details Zonotopes With Large 2D Cuts Zonotopes With Large 2D Cuts

2007-10-16

arxiv.org/abs/0710.3116v3

Mathematics

Metric Geometry

minor changes; 14 pages, 7 figures; to appear in Discrete and Computational Geometry

Scientific paper

There are d-dimensional zonotopes with n zones for which a 2-dimensional
central section has \Omega(n^{d-1}) vertices. For d=3 this was known, with
examples provided by the "Ukrainian easter eggs'' by Eppstein et al. Our result
is asymptotically optimal for all fixed d>=2.

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