  Recently, we enumerate up to isometry, all locally rigid circle packings on
the unit sphere with number of circles N<12. This problem is equivalent to the
enumeration of irreducible contact graphs. In this paper we show that by using
the list of irreducible graphs can solve various problems of extreme packings
such as the Tammes problem for the sphere and the projective plane, the maximal
contacts problem, Danzer's and other problems on irreducible contact graphs.
