Now for the relationship with the Tutte Coxeter graph. I've printed the "synthemes" (triplets of duads) on triangles, with the mirror image on the back. So I can "Triomino" a labeling of the Tutte Coxeter graph. I've convinced myself that laying down 2 adjacent synthemes conpletely fixes the labeling. Makes sense, there are 720 ways of doing that, and 720 inner automorphisms of the graph.
