  In the early 1990s, a family of combinatorial CW-complexes named
permutoassociahedra was introduced by Kapranov, and it was realized by Reiner
and Ziegler as a family of convex polytopes. The polytopes in this family are
"hybrids" of permutohedra and associahedra. Since permutohedra and associahedra
are simple, it is natural to search for a family of simple permutoassociahedra,
which is still adequate for a topological proof of Mac Lane's coherence. This
paper presents such a family.
