On a question of K. Bezdek and T. Odor on Γ-parallelotops

Á. Horváth

doi:10.1007/bf02330879

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 24: Issue 3

On a question of K. Bezdek and T. Odor on Γ-parallelotops

Author:

Á. Horváth

Á. Horváth Technical University of Budapest Faculty of Mechanical Engineer Department of Geometry 1521 Budapest Hungary 1521 Budapest Hungary

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Pages:: 189–192

Online Publication Date:: 10 Apr 2006

Publication Date:: 23 Jun 1992

Article Category:: Research Article

DOI:: https://doi.org/10.1007/bf02330879

Keywords:: 52A45; 52A20; Γ-parallelotops; lattice packing

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Abstract

K. Bezdek and T. Odor proved the following statement in [1]: If a covering ofE³ is a lattice packing of the convex compact bodyK with packing lattice Λ (K is a Λ-parallelotopes) then there exists such a 2-dimensional sublattice Λ′ of Λ which is covered by the set ∪(K+z∣z ∈ Λ′). (K ∪L(Λ′) is a Λ′-parallelotopes). We prove that the statement is not true in the case of the dimensionsn=6, 7, 8.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)