Tough question. I think the question wants you to consider different orientations of the same pattern as one pattern.

Question: If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct patterns are possible: all sides white, all black, just one side white, just one black, and two sides white and two black. If each side of an octahedron is a white or black equilateral triangle, how many distinct patterns are possible?

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