M Theory Revision

Let us recall that one familiar instance of a hexagon represents the paths in a cube, labelled by monomials in $X$, $Y$ and $Z$. Edges of the hexagon must represent the morphing of one path into another, which is to say a face of the cube. Observe how a 1-circulant and a 2-circulant label three vertices each. We could teach this in kindergarten.