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I figured out a way to fold a regular octagon from a strip of paper (a different method than is in the Hilton/Pedersen book). The key techniques are to fold a strip over itself to get a perpendicular line and to fold the edge down to an earlier fold to bisect an angle. 1/2
I believe an analogous technique will work for any regular 2^n-gon. Here's the 16-gon (and the square which is a very simplified version). 2/2
@divbyzero some time ago I really wanted a regular octagon for some home decoration project. I wish I had known about this! I guess the interesting part for you is starting with a strip, but your two key techniques got me through this version too.
@nilesjohnson Nice! I started down this path looking at knotted strips of paper pulled tight into a polygon. One thing led to another...
@divbyzero oh wow! Now I am intrigued to try the strip version too.
@nilesjohnson The book Build Your Own Polyhedra by Peter Hilton and Jean Pedersen give a variety of ways to make polygons out of strips of paper (and then later polyhedra) https://www.amazon.com/BUILD-POLYHEDRA-SECOND-REVISION-SEYMOUR/dp/020149096X
@divbyzero @nilesjohnson Making such knotted polygons with multiple strips of paper can lead to a nice hands-on demonstration of cosets of subgroups of
@tomhull @nilesjohnson Oh, cool. I have that book in my office. I'll check it out next time I'm in.
