Zur besten Beleuchtung konvexer Polyeder (Q796111)

Let P be a polytope in R'' with m facets. The authors investigate the problem how to find the directions with the property that the orthogonal projections of P in these directions have maximal resp. minimal (n-1)- dimensional measure. It is shown that for the minimum problem \(\left( \begin{matrix} m\\ n-1\end{matrix} \right)\) directions and for the maximum problem \(2^{m-1}-1\) directions need to be investigated. These directions can be specified in terms of the normal vectors and of the (n-1)-dimensional measures of the facets of P. The results are applied to the regular polytopes in \(R^ 3\).