Serious Fun with Flexagons : A Compendium and Guide

1 Introduction; 1.1 General Features; 1.2 Terminology; 1.3 Outline of Book; 1.4 Making Flexagons; 1.4.1 General Assembly Instructions; 1.4.2 The Two Sector First Order Fundamental Square Even Edge Flexagon; 2 Polygon Rings; 2.1 Introduction; 2.1.1 Multiple Polygons; 2.1.2 Combinations; 2.2 Edge Rings of Regular Polygons; 2.2.1 General Properties; 2.2.2 Regular Even Edge Rings; 2.2.3 Regular Odd Edge Rings; 2.2.4 Compound Edge Rings; 2.2.5 Irregular Edge Rings; 2.3 Edge Rings of Irregular Polygons; 2.3.1 General Properties; 2.3.2 Even Edge Rings of Silver and Bronze Triangles; 2.4 Vertex Rings; 2.4.1 General Properties; 2.4.2 Vertex Rings of Squares; 3 Fundamental Nets; 3.1 Introduction; 3.2 First Order Fundamental Edge Nets; 3.3 Second Order Fundamental Edge Nets; 3.4 Fundamental Vertex Nets; 3.5 Fundamental Silver and Bronze Edge Nets; 4 Fundamental Edge Flexagons; 4.1 Introduction; 4.1.1 Standard Face Numbering Sequences; 4.1.2 Truncated Flexagons; 4.2 First Order Fundamental Even Edge Flexagons; 4.2.1 General Properties; 4.2.2 Ring Even Edge Flexagons; 4.2.3 First Order Fundamental Triangle Even Edge Flexagons; 4.2.4 First Order Fundamental Square Even Edge Flexagons; 4.2.5 Detailed Analysis of Flexagons; 4.2.6 First Order Fundamental Pentagon Even Edge Flexagons; 4.2.7 First Order Fundamental Hexagon Even Edge Flexagons; 4.2.8 First Order Fundamental Octagon Even Edge Flexagons; 4.2.9 First Order Fundamental Dodecagon Even Edge Flexagons; 4.3 Second Order Fundamental Odd Edge Flexagons; 4.3.1 General Properties; 4.3.2 Second Order Fundamental Triangle Odd Edge Flexagons; 4.3.3 A Second Order Fundamental Square Odd Edge Flexagon; 4.3.4 A Second Order Fundamental 20-gon Odd Edge Flexagon; 5 Fundamental Skeletal and Point Flexagons; 5.1 Introduction; 5.2 First Order Fundamental Even Skeletal Flexagons; 5.2.1 General Properties; 5.2.2 First Order Fundamental Triangle Even Skeletal Flexagons; 5.2.3 A First Order Fundamental Square Even Skeletal Flexagon; 5.3Fundamental Point Flexagons; 5.3.1 General Properties and Unagons; 5.3.2 The Fundamental Triangle Point Flexagon; 5.3.3 The Fundamental Square Point Flexagon; 5.3.4 Fundamental Pentagon Point Flexagons; 5.3.5 The Fundamental Hexagon Point Flexagon; 5.4 Interleaved Fundamental Point Flexagons; 5.4.1 General Properties; 5.4.2 The Interleaved Fundamental Pentagon Point Flexagon; 5.4.3 An Interleaved Fundamental Enneagon Point Flexagon.; 5.5 Augmented Fundamental Point Flexagons; 5.5.1 General Properties; 5.5.2 An Augmented Fundamental Triangle Point Flexagon; 5.5.3 An Augmented Fundamental Square Point Flexagon; 5.6 Augmented Interleaved Fundamental Point Flexagons; 5.6.1 General Properties; 5.6.2 Augmented Interleaved Fundamental Triangle Point Flexagons; 5.6.3 An Augmented Interleaved Fundamental Square Point Flexagon; 6 Fundamental Compound Edge Flexagons; 6.1 Introduction; 6.2 General Properties; 6.3 Triangular Fundamental Compound Edge Flexagons; 6.3.1 Some Properties; 6.3.2 A Fundamental Square Compound Edge Flexagon; 6.3.3 A Fundamental Pentagon Compound Edge Flexagon; 6.4 A Square-Like Fundamental Compound Edge Flexagon; 6.4.1 Some Properties; 6.4.2 A fundamental hexagon compound edge flexagon; 6.5 Pentagonal Fundamental Compound Edge Flexagons; 6.5.1 Some Properties; 6.5.2 A Fundamental Square Compound Edge Flexagon; 6.5.3 A Fundamental Hexagon Compound Edge Flexagon; 6.6 A Hexagonal Fundamental Compound Edge Flexagon; 6.6.1 Some Properties; 6.6.2 A Fundamental Octagon Compound Edge Flexagon; 6.7 Heptagonal Fundamental Compound Edge Flexagons; 6.7.1 Some Properties; 6.7.2 A Fundamental Hexagon Compound Edge Flexagon; 6.7.3 A Fundamental Decagon Compound Edge Flexagon; 7 Irregular Cycle Flexagons; 7.1 Introduction; 7.2 Irregular Cycle Even Edge Flexagons; 7.2.1 General Properties; 7.2.2 Derivation of Nets; 7.2.3 The Irregular Cycle Square Even Edge Flexagon; 7.2.4 An Irregular Cycle Pentagon Even Edge Flexagon; 7.2.5 Irregular Cycle Hexagon Even Edge Flexagons