A characterization of convex surfaces which are 𝐿-sets

Buchman, E. O.; Valentine, F. A.

doi:10.1090/S0002-9939-1973-0320887-4

A characterization of convex surfaces which are $L$-sets
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by E. O. Buchman and F. A. Valentine PDF

Proc. Amer. Math. Soc. 40 (1973), 235-239 Request permission

Abstract:

If the surface of a bounded three dimensional convex body has the property that each pair of its points can see some third point via the surface, then with a single exception the body must be a finite cone with a convex base. The exceptional shape is that of a solid hexahedron with six triangular plane faces formed as the union of two tetrahedra having a congruent face in common.

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The structure of $L$-sets

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