By introducing twists into the iterated function system that defines the Sierpinski gasket, we are able to construct a unique regular energy form that satisfies a self–similar identity with any prescribed projective weights. Our construction is explicit (involving finding a root of a 4th order polynomial), and we are able to find explicitly a polynomial identity for the algebraic variety containing the smooth manifold of admissible weights. Without the twists, there are obstructions to existence, and a complete description due to Sabot is quite complicated.