  A pebble tree is an ordered tree where each node receives some colored
pebbles, in such a way that each unary node receives at least one pebble, and
each subtree has either one more or as many leaves as pebbles of each color. We
show that the contraction poset on pebble trees is isomorphic to the face poset
of a convex polytope called pebble tree polytope. Beside providing intriguing
generalizations of the classical permutahedra and associahedra, our motivation
is that the faces of the pebble tree polytopes provide realizations as convex
polytopes of all assocoipahedra constructed by K. Poirier and T. Tradler only
as polytopal complexes.
