Theory Update 42

If the total of path weights on the edges of a tetractys is $27$ (the number of three qutrit paths) then the total of the vertex weights (where each incoming edge counts once) must be $54$, since each edge has two bounding vertices. The number $27$ is the dimension of a nice Jordan algebra, and $54$ is the dimension of a complexification of the algebra. Using dual honeycombs, the vertices become two dimensional regions.