2018/10/13 by Zili Wang, Wang, Zili
Computer Science · Mathematics · #Algorithm #Combinatorics #Computational Geometry and Mesh Generation #Computer science #Cone (formal languages) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry #Mathematics #Mathematics and Applications #Octahedron #Physics #Point processes and geometric inequalities #Polyhedron #Regular polygon #Set (abstract data type) #Tetrahedron #math.GT
paper · pdf · doi:10.48550/arxiv.1810.05926
11 pages, 4 figures
openalex publication_date 2018/10/13 · arxiv created 2018/11/16 · arxiv updated 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the set of shapes of centrally symmetric octahedra with prescribed cone-deficits. We show that this set forms a real hyperbolic ideal tetrahedron, whose dihedral angles are half of the prescribed cone-deficits.