P -Associahedra

For each poset P , we construct a polytope 𝒜(P) called the P - associahedron . Similarly to the case of graph associahedra, the faces of 𝒜(P) correspond to certain nested collections of subsets of P . The Stasheff associahedron is a compactification of the configuration space of n points on a line, and we recover 𝒜(P) as an analogous compactification of the space of order-preserving maps P→ℝ . Motivated by the study of totally nonnegative critical varieties in the Grassmannian, we introduce affine poset cyclohedra and realize these polytopes as compactifications of configuration spaces of n points on a circle. For particular choices of (affine) posets, we obtain associahedra, cyclohedra, permutohedra, and type B permutohedra as special cases.