  We study proportions of consecutive occurrences of permutations of a given
size. Specifically, the feasible limits of such proportions on large
permutations form a region, called feasible region. We show that this feasible
region is a polytope, more precisely the cycle polytope of a specific graph
called overlap graph. This allows us to compute the dimension, vertices and
faces of the polytope.
  Finally, we prove that the limits of classical occurrences and consecutive
occurrences are independent, in some sense made precise in the extended
abstract. As a consequence, the scaling limit of a sequence of permutations
induces no constraints on the local limit and vice versa.
