I am going back to color symmetries of the Stampfli tiling. In an earlier post I showed a two-color symmetry in rotation. Now I am discussing a symmetry with three colors.
A rotation of the tiling by 30 degrees should change the first color (say red) to the second color (blue), the second color to the third one (green) and the third to the first color. This is not possible for the equilateral triangle because it is mapped onto itself by four rotations of 30 degrees changing red into blue into green. Thus it would have to have all colors at once and I am just using grey. The orientation of the diagonal of the squares and rhombs determines their colors. Then I get this: