  We characterize those unions of embedded disjoint circles in the 2-sphere
which can be the multiple point set of a generic immersion of the 2-sphere into
3-dimensional space in terms of the interlacement of the given circles. Our
result is the one higher dimensional analogue of Rosenstiehl's characterization
of words being Gauss codes of self-crossing plane curves. Our proof uses a
result of Lippner and we further generalize the ideas of Fraysseix and Ossona
de Mendez, which leads us to directed interlacement graphs of paired trees and
their local complementation.
