On the group of isometries of the hyperbolic dodecahedron space of Seifert-Weber. (Russian) Zbl 0635.57006

Mednykh, A. D.

Sib. Mat. Zh. 28, No. 5(165), 134-144 (1987).

Let M be the hyperbolic dodecahedron space of Seifert-Weber. The author proves that all isometries of M preserve orientation and constructs an explicit isomorphism of Isom(M) onto the symmetric group \(S_ 5\). The natural action of Isom(M) on \(H_ 1(M)\) is computed and shown to be faithful.

Reviewer: V.Turaev

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
51M10	Hyperbolic and elliptic geometries (general) and generalizations

Keywords:

hyperbolic dodecahedron space; isometries; symmetric group; action of Isom(M) on \(H_ 1(M)\)