Abstract
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 easter eggs” by Eppstein et al. Our result is asymptotically optimal for all fixed d≥2.
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The authors are supported by Deutsche Forschungsgemeinschaft, via the DFG Research Group “Polyhedral Surfaces,” and a Leibniz grant.
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Rörig, T., Witte, N. & Ziegler, G.M. Zonotopes with Large 2D-Cuts. Discrete Comput Geom 42, 527–541 (2009). https://doi.org/10.1007/s00454-008-9088-4
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DOI: https://doi.org/10.1007/s00454-008-9088-4