We start by studying the magic star.
The centre of the star carries, first of all, the e6 Lie algebra. But being motivically minded, we would like to see e6 hiding in the combinatorial data attached to the plane. Let us begin by blowing up a central point, meaning blow ups to further tetractys tiles. Now the magic star look like this:
which is nice, because the hexagon in the middle of the star is labeled with the 78 paths shown above, giving the dimension of e6, whose polytope is somehow drawing itself. Now we need to understand why the single node at the centre of the hexagon disappears, when the three lines braid instead of intersecting.