Convex polytopes whose projection bodies and difference sets are polars |
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Authors: | Horst Martini |
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Institution: | 1. Sektion Mathematik, P?dagogische Hochschule, Wigardstrasse 17, DDR-8060, Dresden, German Democratic Republic
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Abstract: | In a paper by the author and B. Weissbach it was proved that the projection body and the difference set of ad-simplex (d≥2) are polars. Obviously, ford=2 a convex domain has this property if and only if its difference set is bounded by a so-called Radon curve. A natural question
emerges about further classes of convex bodies inR
d
(d≥3) inducing the mentioned polarity. The aim of this paper is to show that a convexd-polytope (d≥3) is a simplex if and only if its projection body and its difference set are polars. |
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Keywords: | |
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