Flexagons are flexible polygons folded from strips of paper (e.g. see post

viewtopic.php?f=1&t=9831). They come in many different shapes and there are lots of different flexes you can do, where a flex is analogous to rotating a portion of a typical twisty puzzle. Think of them as a twisty puzzle you can fold up and put in your pocket, with similarities to folding a Rubik’s Magic. Figuring out new ways to solve one can involve discovering new flexes as well as new sequences of flexes. And to make matters more interesting, each flex changes the structure of the flexagon, making it so the set of possible flexes change dramatically with each move.

Flexagons have been around for quite awhile, but recently I’ve figured out a bunch of new ways to make interesting puzzles that are a lot like working with a polyhedral twisty puzzle. The most well known of the flexagons is the hexaflexagon, with six equilateral triangles arranged in a hexagon. But you can make a flexagon from any polygon and fold them into many different shapes. Only two sides are visible at any given time, but an arbitrary number of sides can be hidden. I’ve concentrated primarily on triangle flexagons because it’s easier to have five or more polygons per face, which makes for a large variety of flexes. Plus triangles allow such flexagons to lie flat in many configurations.

A sampling of triangle flexagons:

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Puzzles on flexagons:

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Some of the other possible flexagons:

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To give you an idea of what it’s like to manipulate one of these puzzles, here are links to videos of several interesting flexagons from my youtube channel

http://www.youtube.com/user/loki3dot:

For a collection of flexagon templates you can make yourself, a list of some of the flexes and description of the notation I use to describe flex sequences, you can go to my web site,

http://loki3.com/flex/.

I know these are a bit different from the other puzzles here, but they have enough similarities that I thought this group would enjoy them.

- Scott Sherman