Zonotopes with Large 2D-Cuts

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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Veröffentlicht in:	Discrete & computational geometry 2009-12, Vol.42 (4), p.527-541
Hauptverfasser:	Rörig, Thilo, Witte, Nikolaus, Ziegler, Günter M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Computational Mathematics and Numerical Analysis Geometry Mathematics Mathematics and Statistics Polytopes
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	0179-5376 1432-0444
DOI:	10.1007/s00454-008-9088-4