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It bothers me that it's not really 3 times as many unless you only count the small white triangles.
If I'm counting right it's actually X3+2 right? You are adding the inner black triangle and a new overarching triangle.
Yup those are the ones I was thinking of.
And the two black triangles in the corners
not quite. if you were counting the black triangles in the previous iteration, then this should be three times as many triangles, minus three. each of the previous iteration has those two big black triangles in the corner, but when you assemble them together, they merge into the two big corner triangles and the central triangle.
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