On the illumination of a class of convex bodies





Boltyanski’s illumination problem, convex hull, illumination number, Hadwiger’s covering problem


We study Boltyanski’s illumination problem (or Hadwiger's covering problem) for the class of convex bodies in $\mathbb{R}^n$ consisting of convex hulls of a pair of compact convex sets contained in two parallel hyperplanes of $\mathbb{R}^n$. This special case of the problem is completely solved when $n=3$.


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