  We analyse Lieb-kagom\'e model, a three-band model with contact points
showing particular examples of the merging of Dirac contact points. We prove
that eigenstates can be parametrized in a classification surface, which is a
hypersurface of a 4-dimension space. This classification surface is a powerful
device giving topological properties of the energy band structure; the analysis
of its fundamental group proves that all singularities of the band structure
can be characterized by four independent winding (integer) numbers. Lieb case
separates: its classification surface differs and there is only one winding
number.
