Summary: Shadows and slices of polytopes
Nina Amenta \Lambda
Xerox PARC
3333 Coyote Hill Road
Palo Alto, CA 94304, USA
amenta@parc.xerox.com
G¨unter M. Ziegler \Lambda\Lambda
Dept. Mathematics 6­1
Technische Universit¨at Berlin
10623 Berlin, Germany
ziegler@math.tu­berlin.de
http://www.math.tu­berlin.de/¸ziegler
Abstract
We give a lower bound of \Omega\Gamma f bd=2c ) for the
number of vertices of a d­dimensional poly­
tope with f facets which can appear on the
outer boundary of a projection to any di­
mension 2 Ÿ k ! d. By duality, this implies
a lower bound of \Omega\Gamma n bd=2c ) for the num­
ber of facets in a k­dimensional slice of a

Source: Amenta, Nina - Department of Computer Science, University of California, Davis

Collections: Biology and Medicine; Computer Technologies and Information Sciences