Another realization, due to Jean-Louis Loday, is based on the correspondence of the vertices of the associahedron with n-leaf rooted binary trees, and directly produces integer coordinates in (n − 2)-dimensional space. The ith coordinate of Loday's realization is aibi, where ai is the number of leaf descendants of the left child of the ith internal node of the tree (in left-to-right order) and bi is the number of leaf descendants of the right child..
