Dissecting the 2-sphere by immersions

The self intersection of an immersion i : S-2 -> R-3 dissects S-2 into pieces which are planar surfaces ( unless i is an embedding). In this work we determine what collections of planar surfaces may be obtained in this way. In particular, for every n we construct an immersion i: S-2 -> R-3 with 2n triple points, for which all pieces are discs.