Convex polytopes from nested posets

Motivated by the graph associahedron K G , a polytope whose face poset is based on connected subgraphs of G , we consider the notion of associativity and tubes on posets. This leads to a new family of simple convex polytopes obtained by iterated truncations. These generalize graph associahedra and nestohedra, even encompassing notions of nestings on CW-complexes. However, these poset associahedra fall in a different category altogether than generalized permutohedra.