Can I tile a surface with triangles with colored sides so that adjacent sides match in color?

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A bit more detail: I am generating a list of all 3-color combination from a list of colors (say 10, but can increase/decrease). I am generating triangles with these combinations, where each side has one of the 3 colors.

I want to tile a flat surface with these 3-color triangles, but I also want sides that are adjacent (from two neighboring triangles) to share the same color. And, finally, each combination should be repeated just once over the surface. I am also happy to hear a solution that doesn't depend on colors/geometry but numbers of course. I just don't know how to phrase it that way.

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You're looking for MacMahon triangles.