标题： 凸双曲多面体和球面内接凸多面体的特征 显示英文标题

标题： A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere

摘要： 我们描述了Rivin提出的在$\h^3$中凸多面体的表征，该表征基于其二面角。 我们还描述了该理论的一些几何和组合后果。 其中一个后果是，在$\E^3$中所有顶点都位于单位球面上的凸多面体的组合表征。 这解决了Jakob Steiner在1832年提出的一个问题。 显示英文摘要

摘要： We describe a characterization of convex polyhedra in $\h^3$ in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of these consequences is a combinatorial characterization of convex polyhedra in $\E^3$ all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832.