  A positroid is a special case of a realizable matroid that arose from the
study of the totally nonnegative part of the Grassmannian by Postnikov. In this
paper, we study the facets of its matroid polytope and the independent set
polytope. This allows one to describe the bases and independent sets directly
from the decorated permutation, bypassing the use of the Grassmann necklace. We
also describe a criterion for determining whether a given cyclic interval is a
flat or not using the decorated permutation, then show how it applies to
checking the concordancy of positroids.
