© 2009

Serious Fun with Flexagons

A Compendium and Guide

  • Authors


  • Further analysis has led to a much better understanding of the dynamic behaviour of flexagons, from a serious mathematics viewpoint

  • Includes extensive information on the mathematical background to various types of flexagons and their relationships to each other

  • A geometric approach is used throughout, and the book is profusely illustrated

  • Geometric and aesthetic aspects of flexagons can only be fully appreciated by manipulating paper models. Nets and assembly instructions for numerous flexagons are therefore included


Part of the Solid Mechanics and Its Applications book series (SMIA, volume 164)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Les Pook
    Pages 1-14
  3. Les Pook
    Pages 15-31
  4. Les Pook
    Pages 33-41
  5. Les Pook
    Pages 43-76
  6. Les Pook
    Pages 103-118
  7. Les Pook
    Pages 119-145
  8. Les Pook
    Pages 147-174
  9. Les Pook
    Pages 175-200
  10. Les Pook
    Pages 201-245
  11. Les Pook
    Pages 247-298
  12. Les Pook
    Pages 299-323
  13. Back Matter
    Pages 325-329

About this book


A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types.

This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.




Derivation History of Mathematics calculus flexagons geometry history mathematics model

About the authors

Since my formal retirement in 1998 I have been a Visiting Professor in the Department of Mechanical Engineering at University College London, where I do some part time teaching in the fields of metal fatigue and fracture mechanics. I am a senior official of the European Structural Integrity Society, and have been involved with the organisation of two of their conferences (FCP 2003 and CP 2006), including editing conference proceedings and associated special issues of journals.

Bibliographic information


From the reviews:

“This book comes across as a sort of encyclopedia or a classification of flexagons. … The more serious researcher … will find this book an amazing resource for various kinds of flexagons. … I’m sure this book will remain a reference book of choice in the subject of flexagons for a long time. … If you are looking for … ‘Encyclopedia of Flexagons’ this flexagon book appears to be the best on the market.” (Collin Carbno, The Mathematical Association of America, December, 2009)