This tiling is one of the possible variants of a rule given in [WSI95]. Unfortunately the definition given there is not unique. Patches of this rule are not the same as the patches given in the paper. If anyone finds the correct orientations of the thin rhombs then this page will be updated.
Watanabe Ito Soma 12-fold (variant) is another version of this rule (though not one given in the paper), with more symmetry.