volume 29, issue 4, P561-573 2003
DOI: 10.1007/s00454-002-0790-3
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## Abstract: Generalizing the characteristic intersection property of Choquet simplices, it is proved that for line-free convex bodies B 1 and B 2 in E d , the following conditions are equivalent: (i) there is a line-free convex body B ⊂ E d such that every nonempty intersectionis a homothetic copy of B, (ii) both B 1 and B 2 are Choquet simplices and the nonempty intersections B 1 ∩ (v + B 2 ), v ∈ E d , are homothetic copies of a Choquet simplex B. All such triplets B 1 , B 2 , B are described.

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