The author gives a negative answer to the question: are the transformations isomorphic to isometric rearrangement of a finite number of geometric figures typical? This problem arose in connection with the result of Chaika and Davis, which says that interval exchange transformations are not typical. For a compact set of actions, an entropy of Kushnirenko type is chosen, by the author, in such a way that it vanishes on this set but takes infinite values for the typical actions. As a consequence the author finds that typical measure-preserving transformations are not isomorphic to isometric rearrangements of a finite set of geometric figures. The author concludes with several related questions about the values of the $P$-entropy for factors of a typical transformation.