Mednykh, A. D. On the group of isometries of the hyperbolic dodecahedron space of Seifert-Weber. (Russian) Zbl 0635.57006 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 Cited in 1 ReviewCited in 2 Documents 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 \(H_ 1(M)\) PDF BibTeX XML Cite \textit{A. D. Mednykh}, Sib. Mat. Zh. 28, No. 5(165), 134--144 (1987; Zbl 0635.57006) Full Text: EuDML OpenURL