Abstract
In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional Euclidean space. As a consequence, we prove that an parallelepiped with relation \(1:1:\sqrt{2}\) for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter.
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Nikonorov, Y.G., Nikonorova, Y.V. The Intrinsic Diameter of the Surface of a Parallelepiped. Discrete Comput Geom 40, 504–527 (2008). https://doi.org/10.1007/s00454-007-9037-7
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DOI: https://doi.org/10.1007/s00454-007-9037-7