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.


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