  The nonnegative Grassmannian is a cell complex with rich geometric,
algebraic, and combinatorial structures. Its study involves interesting
combinatorial objects, such as positroids and plabic graphs. Remarkably, the
same combinatorial structures appeared in many other areas of mathematics and
physics, e.g., in the study of cluster algebras, scattering amplitudes, and
solitons. We discuss new ways to think about these structures. In particular,
we identify plabic graphs and more general Grassmannian graphs with polyhedral
subdivisions induced by 2-dimensional projections of hypersimplices. This
implies a close relationship between the positive Grassmannian and the theory
of fiber polytopes and the generalized Baues problem. This suggests natural
extensions of objects related to the positive Grassmannian.
