My first introduction to flexagons, Richard Feynman, Martin Gardner, Scientific American magazine and topology happened when I was quite young and bedridden for a long time because of a sledding accident (“hey, is that a fence post I am heading for?”).
My dad, a plastics engineer, had read about these interesting “toys” and made several hexahexaflexagons out of paper to keep me entertained. He also tracked down some of the papers Gardner, Feynman and the actual discoverer, Arthur H. Stone had written about the theory of flexagons.
The math was a little thick for a twelve-year-old, and but some of it eventually sunk in my head. I quickly wore out the paper ones my dad made, so together we figured out a way to make them of a flexible plastic material. These lasted for years.
Without having a flexagon in your hand, it is a little difficult to figure out how it works. The pictures and animation help a little, but make one and see for yourself. Please note that flexagons are not the little origami four-section contraption kids fold, number and put over four fingers to play games with.
The first video explains the basic construction of a 2-dimensional flexagon, and includes a link to template that can be downloaded and printed (probably a better idea for beginners rather than drawing your own). The basic model as be elaborated on quite a bit, and, for example, the second video shows how make a 3D flexagon.
Now go get your week started!