Geodesic
On affine diameters of a convex body
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 39-41 
V. V. Makeev; M. Yu. Zvagel'skii. On affine diameters of a convex body. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 39-41. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a5/
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     author = {V. V. Makeev and M. Yu. Zvagel'skii},
     title = {On affine diameters of a~convex body},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that any convex body in $\mathbb R^n$ has $n$ mutually orthogonal affine diameters $d_1,\dots,d_n$ such that it is possible to shift each of them through a linear combination of direction vectors of the diameters with smaller numbers so that their translates will intersect at their common middle point.

[1] B. Gryunbaum, Etyudy po kombinatornoi geometrii i teorii vypuklykh tel, Nauka, M., 1971 | MR

[2] V. V. Makeev, “Spetsialnye konfiguratsii ploskostei, svyazannye s vypuklym kompaktom”, Zap. nauchn. semin. POMI, 252, 1998, 165–174 | MR | Zbl

[3] V. V. Makeev, “Ob affinnykh diametrakh i khordakh vypuklykh kompaktov”, Zap. nauchn. semin. POMI, 299, 2003, 252–261 | MR | Zbl

[4] V. V. Makeev, “O peresecheniyakh affinnykh diametrov vypuklogo tela”, Ukr. geom. sb., 33 (1990), 70–73 | MR | Zbl

[5] V. P. Soltan, “Affine diameters of convex bodies”, Survey Exp. Math., 23:1 (2005), 47–63 | DOI | MR | Zbl