So before I get too lost again and stuff up my notation, what the notation lets me do is define an abstract topological slice, apart from the real slices meeting at the centre, or partly meeting--it doesn't matter because you see little of the inner surfaces, the relations between these are expressed (algebraically!) on a surface. The slice is the one each octant's inner surfaces is on as it rotates three times, under a \( \mathbb Z_3 \) action on vertex orientations. Its multiplicative version is the equivalent of addition modulo 3, but with complex roots of unity. These roots are tied to a well-known set of polynomials, or to the cyclotomic numbers. But I seem to have a lot of these with prime degree. The graph gets to x = 11 along that axis. So how many primes are there less than 11 (there's a well known formula that tells you), and what can I do with a set of primes less than or equal to 11?