An explicit construction for neighborly centrally symmetric polytopes

Details An explicit construction for neighborly centrally symmetric polytopes An explicit construction for neighborly centrally symmetric polytopes

2006-06-29

arxiv.org/abs/math/0606748v1

Mathematics

Metric Geometry

9 pages, no figures

Scientific paper

We give an explicit construction, based on Hadamard matrices, for an infinite
series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional
polytopes with 4d vertices. This appears to be the best explicit version yet of
a recent probabilistic result due to Linial and Novik, who proved the existence
of such polytopes with a neighborliness of d/400.

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