Zonotopes with Large 2D-Cuts
Thilo Rörig1 
, Nikolaus Witte1 and Günter M. Ziegler1
| (1) |
MA 6–2, Inst. Mathematics, Technische Universität Berlin, 10623 Berlin, Germany |
Received: 26 October 2007 Revised: 21 May 2008 Accepted: 23 May 2008 Published online: 21 June 2008
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.
Keywords Zonotopes - Cuts - Projections - Complexity - Ukrainian easter egg
The authors are supported by Deutsche Forschungsgemeinschaft, via the DFG Research Group “Polyhedral Surfaces,” and a Leibniz
grant.
References secured to subscribers.