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On a Conjecture of Melzak

  • G. C. Shephard (a1)

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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.

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References

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1. Klee, V., Polyhedral sections of convex bodies. Acta Math. 103 (1960), 243267.
2. Meizak, Z.A., A property of convex pseudopolyhedra. Canadian Bull. Math. 2(1959), 3132.
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On a Conjecture of Melzak

  • G. C. Shephard (a1)

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