# Serious Fun with Flexagons

## A Compendium and Guide

• Authors
• L.P. Pook
Book

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

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 77-101
7. Les Pook
Pages 103-118
8. Les Pook
Pages 119-145
9. Les Pook
Pages 147-174
10. Les Pook
Pages 175-200
11. Les Pook
Pages 201-245
12. Les Pook
Pages 247-298
13. Les Pook
Pages 299-323
14. Back Matter
Pages 325-329

### Introduction

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.

### Keywords

Derivation History of Mathematics calculus flexagons geometry history mathematics model