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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