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Here is an interesting concept for a hexagon of 6 sides:

Since the inside angels of all triangles must add up to 180 degs., and the hexagon is an equilateral triangle with each inside angel at 60 degs., and all three sides are the same length. Therefore, the inside cut length is equal to the length of the radius and the angle is 30 degs.

A = 60
R = 1.5
2X = 2 (r cos (a)) = 1.5 = R

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