How to find all the faces...

I didn't want to spoil your fun by telling you this directly, before you had a chance to try on your own ;)

The easiest way to find all the faces in a flexagon is to keep flexing at the same corner, until you can't go any further.

Now change to the next corner. In this way you'll uncover all the faces sooner or later.

The faces appear in a set order - it's called a Tuckerman traverse, named after the guy who found it.

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