ON SOME POLYHEDRA OF FINITE VOLUME IN LOBACHEVSKY SPACE

Muzyka Alexander Andreevich

The work found all crystallographic groups of reflections in Lobachevsky spaces of dimensions 3 and 4, the fundamental polyhedra of which satisfy the following geometric conditions: 1) any two faces of the highest dimension of the fundamental polyhedron M intersect along a face of codimension one or at a point at infinity; 2) all dihedral angles of the polyhedron M are equal to 90°, 60° and 0° (the angle between faces intersecting at a point at infinity) Polyhedra are depicted using Gram graphs. The complete list of such polyhedra contains 16 polyhedra, all of them are non-compact, all polyhedra with exception of two are pyramids.

Keywords:vertex at infinity, face, Gram’s graphs