Shapes of Centrally Symmetric Octahedra with Prescribed Cone-Deficits
Geometric Topology
2018-11-19 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1810.05926,
title = {Shapes of Centrally Symmetric Octahedra with Prescribed Cone-Deficits},
author = {Zili Wang},
journal= {arXiv preprint arXiv:1810.05926},
year = {2018}
}
Comments
11 pages, 4 figures