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Zap. Nauchn. Sem. POMI, 2009, Volume 372, Pages 103–107 (Mi znsl3562)  

This article is cited in 1 scientific paper (total in 1 paper)

On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a three-dimensional centrally symmetric convex body

V. V. Makeev

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: 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 $4/\root3\of3<2.7735$. 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 $4(3+6/(\sqrt3(1+\operatorname{ctg}(\pi/12))))^{2/3}/3<3.2082$. Bibl. – 6 titles.

Key words and phrases: affine-regular hexagon, lattice packing.

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English version:
Journal of Mathematical Sciences (New York), 2011, 175:5, 559–561

UDC: 514.172
Received: 24.01.2008

Citation: V. V. Makeev, “On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a three-dimensional centrally symmetric convex body”, Geometry and topology. Part 11, Zap. Nauchn. Sem. POMI, 372, POMI, St. Petersburg, 2009, 103–107; J. Math. Sci. (N. Y.), 175:5 (2011), 559–561

Citation in format AMSBIB
\Bibitem{Mak09}
\by V.~V.~Makeev
\paper On parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a~three-dimensional centrally symmetric convex body
\inbook Geometry and topology. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 372
\pages 103--107
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3562}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 175
\issue 5
\pages 559--561
\crossref{https://doi.org/10.1007/s10958-011-0368-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958056646}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Makeev, M. Yu. Nikanorova, “Estimating the surface area of spheres in normed spaces”, J. Math. Sci. (N. Y.), 212:5 (2016), 531–532  mathnet  crossref
  • Записки научных семинаров ПОМИ
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