Of affine images of a rhombododecaedron circumscribed about a convex body in $\mathbb R^3$
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 191-195
Voir la notice de l'article provenant de la source Math-Net.Ru
The main result of the paper is dual to an earlier theorem by the author concerning affine images of
a cubeoctahedron inscribed in a three-dimensional convex body. The rhombododecaedron is the
polytope dual to the cubeoctahedron; the latter is the convex hull of the midpoints of the edges of a cube.
Theorem. Every convex body in $\mathbb R^3$ except for those mentioned below admits an affine-circumscribed rhombododecaedron. A possible exception is a body containing a parallelogram $P$ and contained in a cylinder over $P$.
The author does not know whether there is a three-dimensional convex body exceptional on the sense of the above theorem.
@article{ZNSL_1997_246_a11,
author = {V. V. Makeev},
title = {Of affine images of a rhombododecaedron circumscribed about a convex body in $\mathbb R^3$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {191--195},
publisher = {mathdoc},
volume = {246},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a11/}
}
TY - JOUR AU - V. V. Makeev TI - Of affine images of a rhombododecaedron circumscribed about a convex body in $\mathbb R^3$ JO - Zapiski Nauchnykh Seminarov POMI PY - 1997 SP - 191 EP - 195 VL - 246 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a11/ LA - ru ID - ZNSL_1997_246_a11 ER -
V. V. Makeev. Of affine images of a rhombododecaedron circumscribed about a convex body in $\mathbb R^3$. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 191-195. http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a11/