N sided rotation

Suppose I want to create an n sided star. There are other ways to do this, but one way is to rotate the i'th of N copies of a triangle around by 360 * i / N degrees. In other words, just do N way rotational symmetry by rotating the triangle. Ditto if you want N circles in a "ring". Right now, I don't know of any good way to do this. For a fixed N you can jury rig up the right rotations but for arbitrary N? Not so obvious. I can do powers of two up to some fixed limit as in the attached file (and this could be fairly easily extended to, for instance 3 * 2^n) but what about arbitrary N? I thought of generating a "strip" of objects and then using lookup with a gradient to wrap the strip in a circle but that distorts the objects - the part nearer the center of the ring becomes smaller. I don't want any distortion.

Any ideas on whether this is even possible? You could do a Lua script to just rotate one sector 1/N wide but that wouldn't work with the attached file since the size of the circle can be extended so that it extends beyond 1/N. You ought to be able to pass in a parameter to Lua to tell how wide a sector you want, and this would mostly work. Given my last debacle with Lua where it crashed Macs, though, I'm really leery of using it any more. Anybody think of a way to do it without Lua?

Circle Ring Experiment.ffxml