Geodesic
Approximation of three-dimensional convex bodies by affine-regular prisms
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 126-131

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Let $K\subset\mathbb R^3$ be a convex body of unit volume. It is proved that $K$ contains an affine-regular pentagonal prism of volume $4(5-2\sqrt5)/9>0.2346$ and an affine-regular pentagonal antiprism of volume $4(3\sqrt5-5)/27>0.253$. Furthermore, $K$ is contained in an affine-regular pentagonal prism of volume $6(3-\sqrt5)4.5836$, and in an affine-regular heptagonal prism of volume $21(2\cos\pi/7-1)/44.2102$. If $K$ is a tetrahedron, then the latter estimate is sharp. Bibl. – 8 titles. 
@article{ZNSL_2008_353_a10,
     author = {V. V. Makeev},
     title = {Approximation of three-dimensional convex bodies by affine-regular prisms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--131},
     publisher = {mathdoc},
     volume = {353},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a10/}
}
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V. V. Makeev. Approximation of three-dimensional convex bodies by affine-regular prisms. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 126-131. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a10/