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Hyperideal polyhedra in hyperbolic 3-space. (English) Zbl 1033.52009

The authors consider here hyperideal polyhedra. Thought of as projective polyhedra, these are intersections of the hyperbolic space \(\mathbb{H}^3\) with polyhedra, all of whose vertices lie outside \(\mathbb{H}^3\) (they may lie on the absolute). In this paper, such polyhedra are completely classified up to isometry in terms of their combinatorial types and corresponding dihedral angles.

MSC:

52A55 Spherical and hyperbolic convexity
52B10 Three-dimensional polytopes
51M09 Elementary problems in hyperbolic and elliptic geometries
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