I'm wondering if we can derive these formulas in a graphical way. For example, \$$\Phi\$$, \$$\Psi\$$ and \$$\Theta\$$ are intertwined with \$$1_b, 1_c, 1_f\$$, as two inverted parabolas, and in the formulas, they are alternated. Also, we can draw two straight lines, crossing the wires b-d-c and c-e-f, respectively. Looking at c, the positive-shaped straight line has c-d-b and can be connected to \$$\alpha_{c,d,b}\$$; the negative-shaped straight line can be connected to \$$\alpha^{-1}_{c,e,f}\$$. Maybe this could be helpful with more complex diagrams. Is this procedure correct?