Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are ‘flexed’. Workable paper models of flexagons are easy to make, and entertaining to manipulate. Flexagons have a surprisingly complex mathematical structure and just how a flexagon works is not obvious on casual examination of a paper model. The aesthetic appeal of flexagons is in their dynamic behaviour rather than the static appeal of, say, polyhedra. One of the attractions of flexagons is that it is possible to explore their dynamic behaviour experimentally as well as theoretically. Flexagons may be appreciated at three different levels: firstly as toys or puzzles, secondly as a recreational mathematics topic, and finally as the subject of serious mathematical study. Well made models of simple flexagons can be bought, but they are not widely available.

I first became interested in flexagons in the late 1960s through reading two of Martin Gardner's books. At that time I made numerous paper models of flexagons, and carried out some theoretical analysis. I did try writing up some of the material for publication, but editors showed a marked lack of enthusiasm and I lost interest. In 1997, while browsing in a library I came across a paper on flexagons, and this revived my interest. Fortunately, my collection of flexagon models and associated notes had survived three house moves.