Discrete & Computational Geometry

, Volume 40, Issue 4, pp 504–527 | Cite as

The Intrinsic Diameter of the Surface of a Parallelepiped

Article

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.

Keywords

Convex surface Rectangular parallelepiped Intrinsic distance Intrinsic diameter Surface area 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Rubtsovsk Industrial InstituteRubtsovskRussia

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