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：我们提出球形图的公理化理论，作为研究$\mathbb R^3$中多面体特定组合性质的工具。这些性质在离散与计算几何领域中，针对多面体的美术馆问题及其他与可见性相关的问题中具有核心意义。