Geodesic
Extremal values of the volume of $3$-dimensional parallelepipeds with a given intrinsic diameter
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 44-47 
N. V. Rasskazova. Extremal values of the volume of $3$-dimensional parallelepipeds with a given intrinsic diameter. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 44-47. http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a parallelepiped with relation $a:b:c=1:1:\sqrt2$ for its edge lengths has maximal volume among all rectangular parallelepipeds with a given intrinsic diameter.

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