Go to: Associahedron and associator identities · Publications and Preprints · Markus Rost's Web Page
The diagrams show the 1-skeleton with all 42 vertices and 84 edges.
The 28 edges parallel to the 4th dimension are drawn in green. The others form two opposite embeddings •(...), (...)• of the 3-dimensional associahedron (each with 21 edges) and three 2-cells (two pentagons and one quadrilateral). These yield all the cells parallel to the first 3 dimensions.
The first two diagrams have a plain view (without confusing arrows and labels). The second "shoebox" version reflects the construction of the associahedron as described in the paper The associahedral chain complex and the cubical associahedron.
In the next diagrams the black (as opposed to blue) arrow heads depict for each vertex the "canonical directed path" (Mac Lane 1963 MR 170925 p. 34) to the terminal vertex.
The arrows represent a process •(••) → (••)•. The terminal vertex is ((((01)2)3)4)5 (the red point on the bottom cuboid).
The labels in the last diagram are the Tamari indices as in the diagrams up to dimension 3 in Tamari's diagram.
The images have a high resolution (2040x2337, 2188x2085). Go full screen to marvel at them. To access them directly click on the images or the links above.
Go to: Associahedron and associator identities · Publications and Preprints · Markus Rost's Web Page