  At the beggining of the 80's, H.Masur and W.Veech started the study of
generic properties of interval exchange transformations proving that almost
every such transformation is uniquely ergodic. About the same time, S.Novikov's
school and French mathematicians independently discovered very intriguing
phenomena for classes of measured foliations on surfaces and respective IETs.
For instance, minimality is exceptional in these families. A precise version of
this statement is a conjecture by Novikov. The French and Russian constructions
are very different ones. Nevertheless, in the most simple situation (surfaces
of genus three with two singularities) it was recently observed that both
foliations share the same type of properties. For instance, the space of
minimal parameters is the same, called the Rauzy gasket. However, the precise
connection between these two series of works was rather unclear. The aim of
this paper is to prove that both theories describe in different languages the
same objects. This text provides an explicit dictionary between both
constructions.
