Flexagons

Updated 5 January 2021

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 structure and just how a flexagon works is not obvious on casual examination of a paper model. Flexagons may be appreciated at three different level: firstly as toys or puzzles, secondly as a recreational mathematics topic and finally as the subject of serious mathematical study. Some flexagons are described in the sub pages.

For more flexagons see my books ‘Flexagons inside out and Serious fun with flexagons. A compendium and guide, which are listed on the Publications page.

The book by Peter Hilton and Jean Pedersen ‘A mathematical tapestry’ Cambridge University Press, 2010 includes a chapter on hexaflexagons and octaflexagons. A later chapter describes the application of group theory to the trihexaflexagon. For descriptions of group theory look in the index.

The January 2012 issue of The College Mathematics Journal is a Martin Gardner Special Issue. It includes three papers on flexagons which were introduced to a wide audience 50 years ago by Martin Gardner. For my paper see Gardner 13-cmj011-014-pook

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