@benjohn there certainly _is_ structure of that kind in the Spectre tiling. Indeed that's exactly what's represented in the symbolic tile addresses handled by my transducer system.But it's not so easy to relate it back to geometry. The canonical approach is Arnaud Chéritat's "4d lift" concept, in which you express every vertex of a Spectre tile as a pair of complex numbers, with edges at even multiples of 30° incrementing one of the numbers and odd multiples incrementing the other. Once you do that, the geometry becomes simpler, because you can use a linear transformation (aka a 2×2 complex matrix) to transform the vertices of a tile into the vertices of its deflation or inflation, ascending and descending the hierarchy. This is great for theory, but a royal pain when you try to squash it all back into the plane!