In this note we introduce the problem of illumination of convex bodies in spherical spaces and solve it for a large subfamily of convex bodies. We derive from it a combinatorial version of the classical illumination problem for convex bodies in Euclidean spaces as well as a solution to that for a large subfamily of convex bodies, which in dimension three leads to special Koebe polyhedra.

中文翻译：

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从球面照明到欧几里得照明

在这篇笔记中，我们介绍了球面空间中凸体的照明问题，并解决了一个大的凸体子族的问题。我们从中推导出欧几里得空间中凸体的经典照明问题的组合版本，以及一个大的凸体子族的解决方案，在维度三导致特殊的 Koebe 多面体。