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As far as I know, there is no "regular" 4 pointed star.
However, if you have a 4 pointed star, you can draw a circle through it's inner points and a second circle around its outer points. If we say that the inner circle has radius "r" and the outer circle has radius "R", that the angle, "a", of the star's points are:
a = atan(2r / (R√2 - r)
If the outer circle is twice as big as the inner circle, this becomes:
a = atan(2r / (2r√2 - r) = atan(2 / (2√2-1) = 47.5°
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