A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
Craig D. Hodgson, Igor Rivin, Warren D. Smith
Abstract
We describe a characterization of convex polyhedra in 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 3 all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832.
Create a lesson
Related papers
Each simplex in R4 has a point with at least 14 emanating normals to its boundary
Ivan Nasonov, Gaiane Panina
Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞
Emin Abdullaev
Embedding large subsets of Wasserstein spaces into Banach spaces
Cyril Letrouit, Quentin Mérigot
A Smooth Covariogram and the Transition Between Projection Bodies
J. Haddad, C. H. Jiménez, M. Resende Guedes
Intermediate coverings, random images, and projections
Yunhao Zhao, Yingyu Zhao, Chen Zhou et al.
On the Graph Corresponding to Center of Distances of Metric Space
Oleksiy Dovgoshey, Olga Rovenska