Perfect Delaunay Polytopes in Low Dimensions
Metric Geometry
2007-05-23 v1 Number Theory
Abstract
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one correspondence with arithmetic equivalence classes of positive quadratic functions on the n-dimensional integral lattice that can be recovered, up to a scale factor, from the representations of its minimum. We develop a structural theory of such polytopes and describe all known perfect Delaunay polytopes in dimensions one through eight. We suspect that this list is complete.
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Cite
@article{arxiv.math/0702136,
title = {Perfect Delaunay Polytopes in Low Dimensions},
author = {Mathieu Dutour and Robert Erdahl and Konstantin Rybnikov},
journal= {arXiv preprint arXiv:math/0702136},
year = {2007}
}
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44 pages