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Extremum Properties of the Regular Polyhedra

Published online by Cambridge University Press:  20 November 2018

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1. Historical remarks. In this paper we extend some well-known extremum properties of the regular polygons to the regular polyhedra. We start by mentioning some known results in this direction.

First, let us briefly consider the problem which has received the greatest attention among all the extremum problems for polyhedra. It is the determination of the polyhedron of greatest volume F of a class of polyhedra of equal surface areas F, i.e., the isepiphan problem.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1950

References

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10 For the transformation of the Jacobian into the above simple form I am obliged to Mr. J . Molnár.

11 Cf. the proof in the paper referred to in footnote 4.

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