We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other visibility-related problems in discrete and computational geometry.

翻译：我们提出球面图的公理化理论，作为研究$\mathbb R^3$中多面体某些组合性质的工具。这些性质在离散与计算几何中关于多面体的艺术画廊问题及其他可见性相关问题中具有核心重要性。