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On a 3-Dimensional Isoperimetric Problem

Published online by Cambridge University Press:  20 November 2018

Magelone Kömhoff
Magelone Kömhoff*
Affiliation:
University of Toronto, Toronto, Ontario
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Let L(P) denote the total edge length and A(P) the total surface area of a three-dimensional convex polyhedron P. In [5] it was shown that if P belongs to the set of all polyhedra with triangular faces then for all

with equality if and only if is a regular tetrahedron.

It is not difficult to establish the inequality

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 447 - 449
Copyright
Copyright © Canadian Mathematical Society 1970

References

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5. Kömhoff, M., An isoperimetric inequality for convex polyhedra with triangular faces, Canad. Math. Bull. 11 (1968), 723-727.Google Scholar