6 choose 3 = 20. Hence there are 20 triangles in a hexateron
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It depends on what type of regular polygon. For example: regular triangle, regular pentagon, etc.
A regular polygon that has 180 degrees is an equilateral triangle.
If you want a triangle per each side of a regular hexagon, the answer is 6.
By themselves, only 3: triangle, square and hexagon. But there are combinations: eg octagon + square.