## 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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