checkerboard coloring of tiling with 12-fold rotational symmetry

At the risk of boring you I am showing the results of the checkerboard coloring as discussed in the last post, but now for 12-fold rotational symmetry. Again the stars of rhombs have only one color:


All squares have the same color because all angles are equal as for this coloring of the Ammann-Beenker tiling. But here we get again a rather chaotic result as for 10-fold rotational symmetry.

With a special choice of greys the alternative tiling looks like that:


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