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From other sources. See the preface in Notes on the associator [pdf].
Tamayo Jiménez, Daniel. Inversion and Cubic Vectors for Permutrees. 2023. arXiv:2308.05099v2 [math.CO] (page 4). With reference to the next item.
Stanford Lecture: Don Knuth-"The Associative Law, or the Anatomy of Rotations in Binary Trees", Video, November 30, 1993 (at 53.02)
Geyer, Winfried. On Tamari lattices. Discrete Math. 133 (1994), no. 1-3, 99-122. MR 1298967.
Wow!
The three intermediate 2-cells are well recognizable.
(I only found this drawing in August 2025.)
Jean-Louis Loday / Images (archived home page): Polytope de Stasheff (associahedron) de dimension 4, version cubique (mars 2002)
Loday, Jean-Louis. The diagonal of the Stasheff polytope. Higher structures in geometry and physics, 269-292. Progr. Math., 287, 2011. MR 2762549.
Loday, Jean-Louis. Dichotomy of the addition of natural numbers. Associahedra, Tamari lattices and related structures, 65-79. Progr. Math., 299, 2012. MR 3221534.
Saneblidze, Samson; Umble, Ronald. Diagonals on the permutahedra, multiplihedra and associahedra. Homology Homotopy Appl. 6 (2004), no. 1, 363-411. MR 2118493.
Saneblidze, Samson; Umble, Ronald. Comparing diagonals on the associahedra. Homology Homotopy Appl. 26 (2024), no. 1, 141-149. MR 4723091.
Stasheff, James Dillon. Homotopy associativity of H -spaces. I.
Trans. Amer. Math. Soc. 108 (1963), 275-292. MR 158400.
Jim Stasheff, L∞ and A∞
structures: then and now,
2018, arXiv:1809.02526v2
[math.QA]. MR 3939050.
Not cubical, but very close. (Anyway, these pictures definitely have to be shown.)
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