Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $4/\root3\of3<2.7735$. 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. 
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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/

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