Do you have paper, scissors, markers, and glue handy? Then you're not only ready to go back to school, you're ready for today's post!

Today, you'll learn how to make some fascinating paper toys. They all have a mathematical basis, but we're not going to delve into the math behind them. Today's mission is simply the fun of creating and playing.

Our first toy is called a flexagon. It's a hexagonally-shaped paper toy with 3 sides, even though it only appears to have 2.



You can find patterns and templates for designing your own patterns on the author's site.

A 3-sided shape like that is neat, but what about one with more sides? Shortly after Martin Gardner passed away, James Grime filmed this tribute to him, teaching how to make a square 6-sided flexagon:



If you're wondering just how far you can take these, check out flexagon.net to get an idea. They feature wild variations there, include magic square flexagons, and even dodecaflexagons!

Another wild paper toy is called a kaleiodocycle, which you can think of as a 3-dimensional equivalent to a flexagon. Here's a simple way to create a hexagonal kaleiodocycle from three squares of paper:



If you're up for more of a challenge after that, try making the same model from a single piece of paper: