Tetrahedral recursion as a model for space resonance

So, when I reproduced his diagram I began to notice that this represents a power-of-3 recursive scaling function for a tetrahedron. That is, tetrahedrons nest within themselves a phi-spaced intervals such that the second recursion is equal to the maximally resonant proportion 1:81. I believe this is the significance of the tetrahedron in Greek philosophy - it represents maximum resonance which they used to symbolize fire.