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Shapes of centrally symmetric octahedra with prescribed cone-deficits

  • Zili Wang EMAIL logo
From the journal Advances in Geometry


The space of Euclidean cone metrics on centrically symmetric octahedra with fixed cone angles θi < 2π, with total surface area 1, has a natural hyperbolic metric, and is locally isometric to hyperbolic 3-space. The metric completion of the space is isometric to a hyperbolic ideal tetrahedron whose dihedral angles are half the cone-deficits 2πθi.

MSC 2010: 57M50


I would like to thank my adviser Richard Schwartz, from whom I learned this topic and got many helpful feedbacks on the ideas in and the structure of this article.

  1. Communicated by: J. Ratcliffe


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Received: 2019-01-26
Revised: 2019-06-20
Published Online: 2021-04-16
Published in Print: 2021-04-27

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