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Thanks again to Maestro Michael, making this problem a little more interesting. If you didn’t see my updated code on the other thread, it looks like we have the same results up to the 20-gon. I’ll have to do a timings comparison for our approaches and get back to you about that.
There’s another third approach after Line + Line, and Line + Polygon, which would be Polygon + Polygon. In principle that can be done using RegionDifference and RegionIntersection, but perhaps not to tolerance. For maths purposes Region* should still be considered Experimental. I found another bad bug for RegionCongruent while testing on this data. Perhaps RegionCongruent should split out Polygons and use edge + angle code. But I haven’t taken time yet to guarantee your simplified form sorting the two lists.
Thanks again Michael for “Der Zaubermeister hat über das mickey-mouse-zeug gesprochen”. I’m not entirely critical of ChatGPT, but if this German grammar is incorrect, we’ll have to share the blame.
Edit PS. I don’t want to forget to mention these sort of “Polygon Fragmentation” algorithms, when they work correctly, are also very useful for proving theorems about difficult tilings–for example on this recent thread about David Smith’s hat tile .