IMI/Publicaţii/BASM/Ediţii/BASM n.1 (17), 1995/

On three-dimensional hyperbolic manifolds with icosahedral symmetry. (Russian)

Authors: Damian Florin, Makarov V. S.


Principle idea of our technique of constructing new manifolds is to use geometry of the geodetic boundary and it is illustrated by the following example. We consider two manifolds $ \Cal M^3_1$ and $ \Cal M^3_2$ with the same geodetic boundary $ \Cal M^2$ obtained from truncated rhombic triacontahedron $tRT$ (its 5-hedral vertices are cut) and truncated icosahedron $tI$. We can eliminate the boundary by gluing any two copies of manifolds above with different ways.

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