Extremal values of the volume of 3-dimensional parallelepipeds with a given intrinsic diameter

Rasskazova N. V.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 4.

Abstract:
It  is proved that a parallelepiped with relation \(a:b:c=1:1:\sqrt{2}\) for its edge lengths has maximal volume among all rectangular parallelepipeds with a given intrinsic diameter.

Keywords: rectangular parallelepiped, geodesic (intrinsic) diameter, volume

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