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

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
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