Geodesic
On affine diameters of a convex body
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 39-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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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