This doesn't quite work, @ded_ruckus points out, because there are n-gons that you can't get by cutting a corner off an n-1-gon -- in particular, you can't construct a rectangle from a triangle unless you use the 'triangle' with two right angles and a vertex at infinity.https://twitter.com/St_Rev/status/1122062055475949568 …
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Part of the problem is that the original claim isn't quite true. It's false for non-convex polygons unless you define things very carefully. It's easy to read too much into a set of nice examples!
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.