This is really slick, but it was a bit of a puzzle for me trying to turn it into a paper proof! After a few minutes, I realized that you can do it by induction on the number of vertices: it's trivial for n = 3, and if it holds for n - 1, slice off a corner and see what happens.https://twitter.com/ThingsWork/status/1121857148068065280 …
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But this is another example of a slick idea that's surprisingly tricky (but productive) to pin down, and eventually leads to the idea of a 'connection': https://en.wikipedia.org/wiki/Connection_(mathematics) …
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.