On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 103-107
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Let $K$ be a three-dimensional centrally symmetric compact convex set of unit volume. It is proved that $K$ is contained in a centrally symmetric hexagonal prism or a parallelepiped with volume $4/\root3\of32.7735$. This fact implies that $K$ admits a lattice packing in space with density at least $\root3\of3/4>0.3605$. Furthermore, $K$ is contained in a parallelepiped with volume $4(3+6/(\sqrt3(1+\operatorname{ctg}(\pi/12))))^{2/3}/33.2082$. Bibl. – 6 titles.
@article{ZNSL_2009_372_a9,
author = {V. V. Makeev},
title = {On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {103--107},
publisher = {mathdoc},
volume = {372},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a9/}
}
TY - JOUR AU - V. V. Makeev TI - On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body JO - Zapiski Nauchnykh Seminarov POMI PY - 2009 SP - 103 EP - 107 VL - 372 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a9/ LA - ru ID - ZNSL_2009_372_a9 ER -
%0 Journal Article %A V. V. Makeev %T On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body %J Zapiski Nauchnykh Seminarov POMI %D 2009 %P 103-107 %V 372 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a9/ %G ru %F ZNSL_2009_372_a9
V. V. Makeev. On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 103-107. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a9/