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Click the arrow to see the Flexagon in action.

There's a six sided flexagon in a fun new book called Magic Books & Paper Toys by Esther K. Smith.

It's a distant cousin of the Never Ending Card a.k.a the Flippix.
Start with one picture, pinch the sides into the center like a cootie catcher, open the flaps from the center, reveal a second picture. Repeat for the third picture. Flip the entire thing over and do the same and you see inside out views of the same three pictures. I tried it with snowflakes and kaleidoscope pictures.
It's probably easier to make up a plain paper version and then decorate each hexagon as you flip them open, but since when do I do things the easy way? I wanted to be able to send my design to the printer so I had to figure out how to divide up each design and position the parts so they would work properly. Needless to say, the first time around not all of the segments were facing the proper direction. Whoops.
Want to try?
Download a plain template.

Download a snowflake decorated version.

Print template. If you are making the snowflake one, fold it in half the long way and glue together (put glue on the blank side of the paper). There should be snowflake segments printed on both the front and back of the piece.
Score the sides of each triangle. You will have 10 scored triangles.
Starting at one end, fold the triangles back and forth, accordion style. The white triangle that says "glue" should be on top and visible. If it isn't, unfold your accordion and reverse the direction of the folds.

Now pull the "glue" ends toward each other to make a circle out of the folded up piece. (This is a plain paper version colored orange on one side and blue on the other.)

It will either want to flatten out, looking much like the finished piece, or hump up in the the center so it looks like this.
The two ends that say "glue" should align. Glue them together. Let dry.
Okay, you're done! Push the sides into the center and pull out from the middle to flip through three views. Turn the whole thing over and flip through three more.