Shapes of Centrally Symmetric Octahedra with Prescribed Cone-Deficits
classification
🧮 math.GT
keywords
cone-deficitsprescribedshapescentrallyhyperbolicoctahedrapolyhedrasymmetric
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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.
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