Ko Honda’s Octahedral Relation
This morning at Kirbyfest (Happy Birthday!) Ko Honda gave a talk about his work on developing a contact category. You’ve got an oriented surface (with boundary) together with dividing curves as your objects. Morphisms arise via bypass moves. Ko noticed that the octahedral relation is satisfied:
We see four arcs of the Red dividing curves in a White disk of the surface.
The Green triangles are the exact triangles. The Yellow triangles are the commuting triangles.
You can get the SketchUp model here. The disks remain facing the camera in the horizontal direction by using the “face me” function of a component.
Honda informs me that it is usually called The Octahedral Axiom.