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Thin non‐lattice covering with an affine image of a strictly convex body
Author(s) -
Tóth Gábor Fejes,
Kuperberg Wlodzimierz
Publication year - 1995
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001456x
Subject(s) - mathematics , convex body , lattice (music) , regular polygon , affine transformation , affine space , euclidean geometry , combinatorics , euclidean space , ellipsoid , image (mathematics) , dimension (graph theory) , pure mathematics , geometry , convex hull , artificial intelligence , physics , astronomy , acoustics , computer science
We prove that for every strictly convex body C in the Euclidean space of dimension d ≥3, some aflfine image of C admits a non‐lattice covering of the space, thinner than any lattice covering. We illustrate the general construction with an example of a thin non‐lattice covering ofE 3with certain congruent ellipsoids.