We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid nonbipartite crystallizations up to 30 vertices.2000 Mathematics Subject Classification: 57Q15, 57M15, 57N10.

We improve and extend to the non-orientable case a recent result of Karábaš, Maličký and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra

In this paper, we present a catalogue of all genus two 3-manifolds admitting a contracted triangulation with at most 34 simplexes. Then we give a complete classification of the above manifolds. (2000): 57M05, 57N10, 57M15. Mathematics Subject Classifications

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We construct a family of hyperbolic 3-manifolds whose fundamental groups admit a cyclic presentation. We prove that all these manifolds are cyclic branched coverings of S 3 over the knot 5 2 and we compute their homology groups. Moreover, we show that the cyclic presentations correspond to spines of the manifolds.