Book contents
- Frontmatter
- Contents
- Preface
- List of notation
- Introduction
- 1 Making and flexing flexagons
- 2 Early history of flexagons
- 3 Geometry of flexagons
- 4 Hexaflexagons
- 5 Hexaflexagon variations
- 6 Square flexagons
- 7 Introduction to convex polygon flexagons
- 8 Typical convex polygon flexagons
- 9 Ring flexagons
- 10 Distorted polygon flexagons
- 11 Flexahedra
- References
- Flexagon index
- Subject index
1 - Making and flexing flexagons
Published online by Cambridge University Press: 12 August 2009
- Frontmatter
- Contents
- Preface
- List of notation
- Introduction
- 1 Making and flexing flexagons
- 2 Early history of flexagons
- 3 Geometry of flexagons
- 4 Hexaflexagons
- 5 Hexaflexagon variations
- 6 Square flexagons
- 7 Introduction to convex polygon flexagons
- 8 Typical convex polygon flexagons
- 9 Ring flexagons
- 10 Distorted polygon flexagons
- 11 Flexahedra
- References
- Flexagon index
- Subject index
Summary
As an introduction, nets and assembly instructions are given for two simple flexagons. The nets are laid out full size in a form suitable for photocopying. Nets for other types of flexagon are given later in the book to illustrate various points made. General assembly instructions are given for these nets. The appearance of paper models of flexagons can be improved by colouring and decorating the faces. Some decorative schemes exploit symmetries of flexagons both to create an attractive appearance and to create puzzles.
The ‘pinch flex’ used to manipulate flexagons in order to display different pairs of faces is described. A flexagon is flexed from a main position first to an ‘intermediate position’, and then to another main position. Other types of flex are sometimes used and are described later in the book.
The trihexaflexagon
The net for a paper model of a simple hexaflexagon is shown in Fig. 1.1. This is the trihexaflexagon, which was the first type of flexagon to be discovered. The trihexaflexagon is the simplest possible type of hexaflexagon (Conrad 1960, Conrad and Hartline 1962, Cundy and Rollett 1981, Gardner 1965, Gardner 1988, Hilton and Pedersen 1994, Hilton et al. 1997, Johnson 1974, Kenneway 1987, Laithwaite 1980, Liebeck 1964, McIntosh 2000h, McLean 1979, Madachy 1968, Maunsell 1954, Mitchell 1999, Oakley and Wisner 1957, Pedersen and Pedersen 1973, Wheeler 1958).
To make the trihexaflexagon photocopy the net onto 80 g/m2 paper and cut it out. Crease the lines between triangles to form hinges.
- Type
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- Information
- Flexagons Inside Out , pp. 5 - 13Publisher: Cambridge University PressPrint publication year: 2003