OpenSCAD pointed star module

star.scad

// points = number of points (minimum 3)
// outer  = radius to outer points
// inner  = radius to inner points
module Star(points, outer, inner) {
	
	// polar to cartesian: radius/angle to x/y
	function x(r, a) = r * cos(a);
	function y(r, a) = r * sin(a);
	
	// angular width of each pie slice of the star
	increment = 360/points;
	
	union() {
		for (p = [0 : points-1]) {
			
			// outer is outer point p
			// inner is inner point following p
			// next is next outer point following p

			assign(	x_outer = x(outer, increment * p),
					y_outer = y(outer, increment * p),
					x_inner = x(inner, (increment * p) + (increment/2)),
					y_inner = y(inner, (increment * p) + (increment/2)),
					x_next  = x(outer, increment * (p+1)),
					y_next  = y(outer, increment * (p+1))) {
				polygon(points = [[x_outer, y_outer], [x_inner, y_inner], [x_next, y_next], [0, 0]], paths  = [[0, 1, 2, 3]]);
			}
		}
	}
}

Have you tried it with 3? Won't work - you get a triangle. It won't behave correctly when increasing the number of tips.
This is way simpler:

module Star(p=5, r1=4, r2=10) {
  s = [for(i=[0:p*2]) 
    [
      (i % 2 == 0 ? r1 : r2)*cos(180*i/p),
      (i % 2 == 0 ? r1 : r2)*sin(180*i/p)
    ]
  ];
    
  polygon(s);
}