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On convex polyhedra in Lobachevskii spaces

E. M. Andreev


Abstract: This paper is concerned with the investigation of properties of convex polyhedra in Lobachevskii spaces; it gives a complete description of convex bounded polyhedra with dihedral angles not exceeding $90^\circ$, in a three-dimensional Lobachevskii space. This in turn permits a description of the discrete groups generated by reflections acting in the three-dimensional Lobachevskii space with a compact fundamental region.
Figures: 6.
Bibliography: 6 titles.

UDC: 513.34+513.812

MSC: 52B05, 52B70, 52A15, 51F15, 52A55, 32Q35

Received: 03.06.1969

 English version: Mathematics of the USSR-Sbornik, 1970, 10:3, 413–440

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