Associahedra can be realized by taking the convex hull of coordinates derived from binary trees. Similarly, permutahedra can be found using leveled trees. In this paper we will introduce a new type of painted tree, (T ◦ Y)n where n is the number of interior nodes. We create these painted trees by composing binary trees on leveled trees. We define a coordinate system on these trees and take the convex hull of these points. We explore the resulting polytope and prove, using a bijection to tubings, that for n ≤ 4 the poset of the painted face trees with n+1 leaves is isomorphic to the face poset of an n-dimensional polytope, specifically KF1,n, the graph-associahedron for a fan graph, F1,n.