Tetrahedron manifolds via coloured graphs

Abstract In his paper ‘Tetrahedron manifolds and space forms’, Molnar describes an infinite class of 3-manifolds (depending on two natural integers m , n ) by means of suitable face identifications on a tetrahedron. These manifolds can be represented by edge-coloured graphs. By making use of these combinatorial techniques, it is easy to show that they are 2-fold coverings of the 3-sphere, branched over suitable links. This immediately leads to the classification of these manifolds in terms of Seifert fibered spaces.