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On a Conjecture of Melzak

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
G. C. Shephard*
Affiliation:
University of Birmingham
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Melzak [2] has shown that there exists a convex pseudopolyhedron Q (the convex hull of a convergent sequence of points together with its limit point) in E3 which is s-universal for triangles, that is, all possible triangles occur (up to similarity) as plane sections of Q. He conjectured that no polyhedron P has this property. In this short note we give an elementary proof of this conjecture.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 561 - 563
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Klee, V., Polyhedral sections of convex bodies. Acta Math. 103 (1960), 243–267.CrossRefGoogle Scholar
2. Meizak, Z.A., A property of convex pseudopolyhedra. Canadian Bull. Math. 2(1959), 31–32.Google Scholar