  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.
