Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 183-186
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V. V. Makeev. On inscribing a regular octahedron in a three-dimensional convex body with smooth boundary. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 183-186. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a10/
@article{ZNSL_2001_279_a10,
author = {V. V. Makeev},
title = {On inscribing a regular octahedron in a three-dimensional convex body with smooth boundary},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {183--186},
year = {2001},
volume = {279},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a10/}
}
TY - JOUR
AU - V. V. Makeev
TI - On inscribing a regular octahedron in a three-dimensional convex body with smooth boundary
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 183
EP - 186
VL - 279
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a10/
LA - ru
ID - ZNSL_2001_279_a10
ER -
%0 Journal Article
%A V. V. Makeev
%T On inscribing a regular octahedron in a three-dimensional convex body with smooth boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 183-186
%V 279
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a10/
%G ru
%F ZNSL_2001_279_a10
A norm $\|\cdot\|$ and a convex body $K$ with smooth boundary in the standard Euclidean space $\mathbb R^3$ are considered. It is proved that the boundary $\partial K$ of $K$ contains the vertices $AA'BB'CC'$ of a regular octahedron with $\|AA'\|=\|BB'\|\ge\|CC'\|$ (respectively, $\|AA'\|=\|BB'\|\le\|CC'\|$).
