Perfect Delaunay Polytopes in Low Dimensions

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dc.creatorDutour, Mathieu
dc.creatorErdahl, Robert
dc.creatorRybnikov, Konstantin
dc.date2007-02-06
dc.date.accessioned2026-07-07T07:45:05Z
dc.date.available2026-07-07T07:45:05Z
dc.descriptionA 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.
dc.description44 pages
dc.identifierhttps://arxiv.org/abs/math/0702136
dc.identifierhttp://arxiv.org/abs/math/0702136
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123421
dc.subjectMetric Geometry
dc.subjectNumber Theory
dc.subject11-xx; 52Bxx; 52Cxx
dc.titlePerfect Delaunay Polytopes in Low Dimensions
dc.typetext

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