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Octahedral noncompact hyperbolic space forms with finite volume. (English) Zbl 0891.53008

By pairing faces, via isometries from two groups which act discontinuously and freely on the hyperbolic three-space, of the same regular octahedron with all ideal vertices whose faces form angles \(\pi/2\), the author constructs two new nonorientable, noncompact hyperbolic space forms. These two space forms appear to be isometric.

MSC:

53A35 Non-Euclidean differential geometry
57S30 Discontinuous groups of transformations
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