Simple Graphs
In graph theory a graph is a collection of nodes where connections between the two are shown by lines. This can easily be applied to polygons in order to draw non convex figures. You start off with a regular convex polygon and then to draw the regular star polygons you connect each vertex to another by skipping a certain number of nodes.
If you connect up each node to every other node you get what is called a simple graph which is actually the collection of every regular star polygon drawn on top of each other. Here is that graph for a 16gon. I then filed in the resulting tiling so that no tile is ever touching another filled in tile along an edge. In the first one I then shaded all of those tiles in ROYGBIV color order. In the next two I took the original image and shaded in what ever was left white in ROYGBIV and VIBGYOR color order.
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