What is the definition of dent angle in a star polygon?

Answer 1

The dent angle of a star polygon is the angle formed by the bent line between two points that form the point angles. I found a PDF that defines the way to calculate that dent angle and checked it out with a know star. It works:

For a star polygon with n points and 2n congruent sides and a point angle of A:

the dent angle B = (360/n) + A

So for an 8 pointed star with a point angle of 20 degrees, the formula says:

(360/8) + 20 = 65 degrees

Note that if the point angle is 135 degrees it is really no longer a star polygon because the two (otherwise bent) line between each of the 8 point becomes 180 degrees. The above formula also proves that Equally for an 8 pointed star polygon formed by joining each second point (forming two over lapped squares, the resultant dent angle becomes 135 degrees. Again the formula confirms that angle. Two home-runs feels pretty good!

The URL reference is:

teach.valdosta.edu/plmoch/MATH3162/Spring%202009/11-3.pdf