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Maximum possible number of similar three-colored triangles

I want to maximize the number of similar triangles with vertices from three fixed sets, one vertex from each set. … For the $2\times2\times2$ case, can you find six points $X_1, X_2, Y_1, Y_2, Z_1, Z_2$ such that all eight triangles $X_iY_jZ_k$ are similar? …
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