A catalogue of the genus two 3-manifolds

In this paper, the extension of the notion of “wave move” to crystallizations (by Casali-Grasselli) leads to a “reduced” catalogue of all genus $g\le 2$ 3-manifolds, depending on 6-tuples of positive integers. The appendix shows a partial output of the computer program which generates the catalogue and gives a presentation of the fundamental group of each element.