Here is what @GerardWestendorp got when he folded up this 11-pointed star: a hexagonal antiprism! The top is a regular hexagon, and so is the bottom, but the bottom is rotated 1/12th of a full turn compared to the top. Around the sides there are 12 equilateral triangles.
If you don't know about antiprisms, you can look at some here:
https://en.wikipedia.org/wiki/Antiprism
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