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## Star polytopes and hyperbolic 3-manifolds. (English)

Authors: Damian Florin, Makarov V. S.

### Abstract

A hyperbolic 3-manifold $\Cal M^3$ with symmetry group of order 28 800 is constructed. The map of this manifold is composed from 120 hyperbolic dodecahedra with dihedral angle of $2\pi/5$. It is shown that $\Cal M^3$ is geodesically immersed (with self-intersections) into the hyperbolic 4-dimensional manifold of regular 120-cells $D^4$ (Davis manifold $\Cal D^4$). It is proved that the map of this 3-manifold coincides with the map given by the incidence structure of 3-faces of the 4-dimensional regular star polytope \{5, 3, 5/2\}.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
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