Pook Serious Fun with Flexagons

A Compendium and Guide
1. Auflage 2009
ISBN: 978-90-481-2503-6
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 164, 330 Seiten

Reihe: Solid Mechanics and Its Applications

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.    

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.

Autoren/Hrsg.

Pook, L. P.

Inhaltsverzeichnis

1;162654_1_En_FM1_Chapter_O.pdf;2
2;162654_1_En_1_Chapter_O.pdf;16
2.1;Chapter 1;16
2.1.1;Introduction;16
2.1.1.1;1.1 General Features;16
2.1.1.2;1.2 Terminology;20
2.1.1.3;1.3 Outline of Book;24
2.1.1.4;1.4 Making Flexagons;26
2.1.1.4.1;1.4.1 General Assembly Instructions;27
2.1.1.4.2;1.4.2 The Two Sector First Order Fundamental Square Even Edge Flexagon;28
2.1.2;References;28
3;162654_1_En_2_Chapter_O.pdf;30
3.1;Chapter 2;30
3.1.1;Polygon Rings;30
3.1.1.1;2.1 Introduction;30
3.1.1.1.1;2.1.1 Multiple Polygons;31
3.1.1.1.2;2.1.2 Combinations;32
3.1.1.2;2.2 Edge Rings of Regular Polygons;32
3.1.1.2.1;2.2.1 General Properties;32
3.1.1.2.2;2.2.2 Regular Even Edge Rings;35
3.1.1.2.3;2.2.3 Regular Odd Edge Rings;36
3.1.1.2.4;2.2.4 Compound Edge Rings;38
3.1.1.2.5;2.2.5 Irregular Edge Rings;41
3.1.1.3;2.3 Edge Rings of Irregular Polygons;42
3.1.1.3.1;2.3.1 General Properties;42
3.1.1.3.2;2.3.2 Even Edge Rings of Silver and Bronze Triangles;43
3.1.1.4;2.4 Vertex Rings;44
3.1.1.4.1;2.4.1 General Properties;44
3.1.1.4.2;2.4.2 Vertex Rings of Squares;45
3.1.2;References;46
4;162654_1_En_3_Chapter_O.pdf;47
4.1;Chapter 3;47
4.1.1;Fundamental Nets;47
4.1.1.1;3.1 Introduction;47
4.1.1.2;3.2 First Order Fundamental Edge Nets;48
4.1.1.3;3.3 Second Order Fundamental Edge Nets;48
4.1.1.4;3.4 Fundamental Vertex Nets;50
4.1.1.5;3.5 Fundamental Silver and Bronze Edge Nets;55
4.1.2;References;55
5;162654_1_En_4_Chapter_O.pdf;56
5.1;Chapter 4;56
5.1.1;Fundamental Edge Flexagons;56
5.1.1.1;4.1 Introduction;56
5.1.1.1.1;4.1.1 Standard Face Numbering Sequences;57
5.1.1.1.2;4.1.2 Truncated Flexagons;57
5.1.1.2;4.2 First Order Fundamental Even Edge Flexagons;58
5.1.1.2.1;4.2.1 General Properties;58
5.1.1.2.2;4.2.2 Ring Even Edge Flexagons;63
5.1.1.2.3;4.2.3 First Order Fundamental Triangle Even Edge Flexagons;64
5.1.1.2.4;4.2.4 First Order Fundamental Square Even Edge Flexagons;66
5.1.1.2.5;4.2.5 Detailed Analysis of Flexagons;67
5.1.1.2.5.1;4.2.5.1 Sector Symbols;67
5.1.1.2.5.2;4.2.5.2 Tuckerman Diagrams;68
5.1.1.2.5.3;4.2.5.3 Full Maps;69
5.1.1.2.5.4;4.2.5.4 Flexagon Diagrams;70
5.1.1.2.6;4.2.6 First Order Fundamental Pentagon Even Edge Flexagons;71
5.1.1.2.7;4.2.7 First Order Fundamental Hexagon Even Edge Flexagons;75
5.1.1.2.8;4.2.8 First Order Fundamental Octagon Even Edge Flexagons;77
5.1.1.2.9;4.2.9 First Order Fundamental Dodecagon Even Edge Flexagons;79
5.1.1.3;4.3 Second Order Fundamental Odd Edge Flexagons;81
5.1.1.3.1;4.3.1 General Properties;81
5.1.1.3.2;4.3.2 Second Order Fundamental Triangle Odd Edge Flexagons;82
5.1.1.3.3;4.3.3 A Second Order Fundamental Square Odd Edge Flexagon;85
5.1.1.3.4;4.3.4 A Second Order Fundamental 20-gon Odd Edge Flexagon;87
5.1.2;References;88
6;162654_1_En_5_Chapter_O.pdf;90
6.1;Chapter 5;90
6.1.1;Fundamental Skeletal and Point Flexagons;90
6.1.1.1;5.1 Introduction;90
6.1.1.2;5.2 First Order Fundamental Even Skeletal Flexagons;91
6.1.1.2.1;5.2.1 General Properties;91
6.1.1.2.2;5.2.2 First Order Fundamental Triangle Even Skeletal Flexagons;92
6.1.1.2.3;5.2.3 A First Order Fundamental Square Even Skeletal Flexagon;94
6.1.1.3;5.3 Fundamental Point Flexagons;95
6.1.1.3.1;5.3.1 General Properties and Unagons;95
6.1.1.3.2;5.3.2 The Fundamental Triangle Point Flexagon;96
6.1.1.3.3;5.3.3 The Fundamental Square Point Flexagon;97
6.1.1.3.4;5.3.4 Fundamental Pentagon Point Flexagons;98
6.1.1.3.5;5.3.5 The Fundamental Hexagon Point Flexagon;99
6.1.1.4;5.4 Interleaved Fundamental Point Flexagons;100
6.1.1.4.1;5.4.1 General Properties;100
6.1.1.4.2;5.4.2 The Interleaved Fundamental Pentagon Point Flexagon;102
6.1.1.4.3;5.4.3 An Interleaved Fundamental Enneagon Point Flexagon;103
6.1.1.5;5.5 Augmented Fundamental Point Flexagons;104
6.1.1.5.1;5.5.1 General Properties;104
6.1.1.5.2;5.5.2 An Augmented Fundamental Triangle Point Flexagon;105
6.1.1.5.3;5.5.3 An Augmented Fundamental Square Point Flexagon;106
6.1.1.6;5.6 Augmented Interleaved Fundamental Point Flexagons;108
6.1.1.6.1;5.6.1 General Properties;108
6.1.1.6.2;5.6.2 Augmented Interleaved Fundamental Triangle Point Flexagons;110
6.1.1.6.3;5.6.3 An Augmented Interleaved Fundamental Square Point Flexagon;113
6.1.2;References;114
7;162654_1_En_6_Chapter_O.pdf;115
7.1;Chapter 6;115
7.1.1;Fundamental Compound Edge Flexagons;115
7.1.1.1;6.1 Introduction;115
7.1.1.2;6.2 General Properties;116
7.1.1.3;6.3 Triangular Fundamental Compound Edge Flexagons;119
7.1.1.3.1;6.3.1 Some Properties;119
7.1.1.3.2;6.3.2 A Fundamental Square Compound Edge Flexagon;119
7.1.1.3.3;6.3.3 A Fundamental Pentagon Compound Edge Flexagon;120
7.1.1.4;6.4 A Square-Like Fundamental Compound Edge Flexagon;121
7.1.1.4.1;6.4.1 Some Properties;121
7.1.1.4.2;6.4.2 A Fundamental Hexagon Compound Edge Flexagon;121
7.1.1.5;6.5 Pentagonal Fundamental Compound Edge Flexagons;123
7.1.1.5.1;6.5.1 Some Properties;123
7.1.1.5.2;6.5.2 A Fundamental Square Compound Edge Flexagon;123
7.1.1.5.3;6.5.3 A Fundamental Hexagon Compound Edge Flexagon;124
7.1.1.6;6.6 A Hexagonal Fundamental Compound Edge Flexagon;125
7.1.1.6.1;6.6.1 Some Properties;125
7.1.1.6.2;6.6.2 A Fundamental Octagon Compound Edge Flexagon;125
7.1.1.7;6.7 Heptagonal Fundamental Compound Edge Flexagons;127
7.1.1.7.1;6.7.1 Some Properties;127
7.1.1.7.2;6.7.2 A Fundamental Hexagon Compound Edge Flexagon;127
7.1.1.7.3;6.7.3 A Fundamental Decagon Compound Edge Flexagon;129
7.1.2;References;130
8;162654_1_En_7_Chapter_O.pdf;131
8.1;Chapter 7;131
8.1.1;Irregular Cycle Flexagons;131
8.1.1.1;7.1 Introduction;131
8.1.1.2;7.2 Irregular Cycle Even Edge Flexagons;133
8.1.1.2.1;7.2.1 General Properties;133
8.1.1.2.2;7.2.2 Derivation of Nets;134
8.1.1.2.3;7.2.3 The Irregular Cycle Square Even Edge Flexagon;135
8.1.1.2.4;7.2.4 An Irregular Cycle Pentagon Even Edge Flexagon;138
8.1.1.2.5;7.2.5 Irregular Cycle Hexagon Even Edge Flexagons;139
8.1.1.3;7.3 Irregular Cycle Interleaved Point Flexagons;141
8.1.1.3.1;7.3.1 General Properties;141
8.1.1.3.2;7.3.2 Interleaf Flexes;143
8.1.1.3.3;7.3.3 The Irregular Cycle Interleaved Square Point Flexagon;143
8.1.1.3.4;7.3.4 Irregular Cycle Interleaved Pentagon Point Flexagons;145
8.1.1.3.5;7.3.5 Irregular Cycle Interleaved Hexagon Point Flexagons;147
8.1.1.3.6;7.3.6 Augmented Irregular Cycle Interleaved Triangle Point Flexagons;149
8.1.1.4;7.4 Distinct Face Numbering Sequences;153
8.1.1.5;7.5 Irregular Cycle Non Interleaved Point Flexagons;154
8.1.1.5.1;7.5.1 General Properties;154
8.1.1.5.2;7.5.2 The Irregular Cycle Non Interleaved Square Point Flexagon;155
8.1.1.5.3;7.5.3 An Irregular Cycle Non Interleaved Pentagon Point Flexagon;155
8.1.2;References;157
9;162654_1_En_8_Chapter_O.pdf;158
9.1;Chapter 8;158
9.1.1;Degenerate Flexagons;158
9.1.1.1;8.1 Introduction;158
9.1.1.2;8.2 Degenerate Even Edge Flexagons;160
9.1.1.2.1;8.2.1 General Properties;160
9.1.1.2.2;8.2.2 A Degenerate Square Even Edge Flexagon;162
9.1.1.2.3;8.2.3 Degenerate Pentagon Even Edge Flexagons;163
9.1.1.2.4;8.2.4 Degenerate Hexagon Even Edge Flexagons;165
9.1.1.2.5;8.2.5 Degenerate Octagon Even Edge Flexagons;168
9.1.1.2.6;8.2.6 A Degenerate Dodecagon Even Edge Flexagon;170
9.1.1.3;8.3 Degenerate Non Interleaved Point Flexagons;172
9.1.1.3.1;8.3.1 General Properties;172
9.1.1.3.2;8.3.2 The Degenerate Non Interleaved Square Point Flexagon;174
9.1.1.3.3;8.3.3 Degenerate Non Interleaved Pentagon Point Flexagons;175
9.1.1.4;8.4 Degenerate Irregular Cycle Interleaved Point Flexagons;176
9.1.1.4.1;8.4.1 General Properties;176
9.1.1.4.2;8.4.2 Degenerate Interleaved Triangle Point Flexagons;177
9.1.1.5;8.5 Degenerate Compound Edge Flexagons;180
9.1.1.5.1;8.5.1 General Properties;180
9.1.1.5.2;8.5.2 The Degenerate Square-Like Hexagon Compound Edge Flexagon;182
9.1.1.5.3;8.5.3 Degenerate Pentagonal Compound Edge Flexagons;183
9.1.1.5.3.1;8.5.3.1 A Degenerate Pentagonal Square Compound Edge Flexagon;183
9.1.1.5.3.2;8.5.3.2 A Degenerate Pentagonal Hexagon Compound Edge Flexagon;184
10;162654_1_En_9_Chapter_O.pdf;186
10.1;Chapter 9;186
10.1.1;Irregular Ring Even Edge Flexagons;186
10.1.1.1;9.1 Introduction;186
10.1.1.1.1;9.1.1 Fundamental Irregular Ring Even Edge Flexagons;186
10.1.1.2;9.2 Irregular Ring Triangle Even Edge Flexagons;188
10.1.1.2.1;9.2.1 General Properties;188
10.1.1.2.2;9.2.2 An Irregular Ring 12 Triangle Even Edge Flexagon;188
10.1.1.2.3;9.2.3 An Irregular Ring Eight Triangle Even Edge Flexagon;189
10.1.1.2.4;9.2.4 An Irregular Ring 16 Triangle Even Edge Flexagon;190
10.1.1.3;9.3 Irregular Ring Square Even Edge Flexagons;190
10.1.1.3.1;9.3.1 General Properties;190
10.1.1.3.2;9.3.2 Irregular Ring Six Square Even Edge Flexagons;191
10.1.1.3.3;9.3.3 Irregular Ring Eight Square Even Edge Flexagons;194
10.1.1.4;9.4 Irregular Ring Pentagon Even Edge Flexagons;197
10.1.1.4.1;9.4.1 General Properties;197
10.1.1.4.2;9.4.2 An Irregular Ring Six Pentagon Even Edge Flexagon;198
10.1.1.4.3;9.4.3 An Irregular Ring Eight Pentagon Even Edge Flexagon;201
10.1.1.5;9.5 Irregular Ring Hexagon Even Edge Flexagons;202
10.1.1.5.1;9.5.1 General Properties;202
10.1.1.5.2;9.5.2 An Irregular Ring Six Hexagon Even Edge Flexagon;203
10.1.1.5.3;9.5.3 Irregular Ring Eight Hexagon Even Edge Flexagons;205
10.1.1.6;9.6 Irregular Ring Dodecagon Even Edge Flexagons;208
10.1.1.6.1;9.6.1 General Properties;208
10.1.1.6.2;9.6.2 Irregular Ring Eight Dodecagon Even Edge Flexagons;209
11;162654_1_En_10_Chapter_O.pdf;212
11.1;Chapter 10;212
11.1.1;Irregular Polygon Edge Flexagons;212
11.1.1.1;10.1 Introduction;212
11.1.1.1.1;10.1.1 Transformation of Polygons;213
11.1.1.1.2;10.1.2 Stretch Flexagons and Stretch Polygon Rings;214
11.1.1.2;10.2 Irregular Triangle Edge Flexagons;214
11.1.1.2.1;10.2.1 Irregular Triangles;214
11.1.1.2.2;10.2.2 Isosceles Triangle Edge Rings;215
11.1.1.2.3;10.2.3 Bronze Even Edge Rings;217
11.1.1.2.4;10.2.4 Isosceles Triangle Even Edge Flexagons;218
11.1.1.2.4.1;10.2.4.1 Fundamental Silver Even Edge Flexagons;218
11.1.1.2.4.2;10.2.4.2 The Irregular Ring Ten Silver Triangle Even Edge Flexagon;221
11.1.1.2.4.3;10.2.4.3 A Partial Overlap Silver Even Edge Flexagon;223
11.1.1.2.4.4;10.2.4.4 A Fundamental Cart Wheel Even Edge Flexagon;224
11.1.1.2.4.5;10.2.4.5 A Fundamental Star Ring Even Edge Flexagon;225
11.1.1.2.5;10.2.5 Isosceles Triangle Odd Edge Flexagons;225
11.1.1.2.6;10.2.6 Scalene Triangle Even Edge Flexagons;227
11.1.1.2.6.1;10.2.6.1 Fundamental Bronze Even Edge Flexagons;228
11.1.1.2.6.2;10.2.6.2 The Two Sector Fundamental Bronze Even Edge Flexagon;230
11.1.1.2.6.3;10.2.6.3 The Three Sector Fundamental Bronze Even Edge Flexagon;231
11.1.1.2.6.4;10.2.6.4 The Four Sector Fundamental Bronze Even Edge Flexagon;232
11.1.1.2.6.5;10.2.6.5 The Six Sector Fundamental Bronze Even Edge Flexagon;232
11.1.1.2.6.6;10.2.6.6 The Irregular Ring Eight Bronze Triangle Even Edge Flexagon;238
11.1.1.2.7;10.2.7 A Partial Overlap Bronze Even Edge Flexagon;239
11.1.1.2.8;10.2.8 A Scalene Triangle Even Edge Flexagon;240
11.1.1.3;10.3 Irregular Quadrilateral Even Edge Flexagons;242
11.1.1.3.1;10.3.1 Irregular Quadrilaterals;242
11.1.1.3.2;10.3.2 Irregular Quadrilateral Even Edge Rings;243
11.1.1.3.3;10.3.3 A Rectangle Even Edge Flexagon;244
11.1.1.3.4;10.3.4 Rhombus Even Edge Flexagons;246
11.1.1.3.4.1;10.3.4.1 A 60°–120° Rhombus Even Edge Flexagon;246
11.1.1.3.4.2;10.3.4.2 Irregular Ring Rhombus Even Edge Flexagons;247
11.1.1.3.4.3;10.3.4.3 A Partial Overlap 60°–120° Rhombus Even Edge Flexagon;249
11.1.1.3.5;10.3.5 A Trapezium Even Edge Flexagon;250
11.1.1.4;10.4 Irregular Pentagon Even Edge Flexagons;251
11.1.1.4.1;10.4.1 Irregular Pentagons;251
11.1.1.4.2;10.4.2 Irregular Pentagon Even Edge Rings;252
11.1.1.4.3;10.4.3 An Equiangular Irregular Pentagon Even Edge Flexagon;253
11.1.1.4.4;10.4.4 An Irregular Ring Eight Irregular Pentagon Even Edge Flexagon;255
11.1.2;References;255
12;162654_1_En_11_Chapter_O.pdf;257
12.1;11;257
12.1.1;Complex Flexagons;257
12.1.1.1;11.1 Introduction;257
12.1.1.2;11.2 Linked Even Edge Flexagons;259
12.1.1.2.1;11.2.1 Methods of Linking;259
12.1.1.2.2;11.2.2 Linked Hexaflexagons;261
12.1.1.2.3;11.2.3 Linked Square Even Edge Flexagons;265
12.1.1.2.3.1;11.2.3.1 Square Even Edge Flexagons with Flat Main Position Links;266
12.1.1.2.3.2;11.2.3.2 Square Even Edge Flexagons with Box Position Links;268
12.1.1.2.4;11.2.4 Linked Pentagon Even Edge Flexagons;272
12.1.1.2.4.1;11.2.4.1 A Pentagon Even Edge Flexagon with a Skew Main Position Link;273
12.1.1.2.4.2;11.2.4.2 A Pentagon Even Edge Flexagon with a Pair of Slant Main Position Links;274
12.1.1.2.5;11.2.5 Linked Silver Even Edge Flexagons;275
12.1.1.2.5.1;11.2.5.1 General Properties;275
12.1.1.2.5.2;11.2.5.2 A Silver Even Edge Flexagon with a Flat Main Position Link;275
12.1.1.2.5.3;11.2.5.3 An Uncut Silver Even Edge Flexagon with a Flat Main Position Link;277
12.1.1.2.5.4;11.2.5.4 A Silver Even Edge Flexagon with a Skew Main Position Link;279
12.1.1.2.6;11.2.6 Linked Bronze Even Edge Flexagons;281
12.1.1.2.6.1;11.2.6.1 General Properties;281
12.1.1.2.6.2;11.2.6.2 A Bronze Even Edge Flexagon with a Skew Main Position Link;281
12.1.1.2.6.3;11.2.6.4 An Uncut Bronze Even Edge Flexagon with a Flat Main Position Link;286
12.1.1.3;11.4 Conjoined Point Flexagons;292
12.1.1.3.1;11.4.1 General Properties;292
12.1.1.3.2;11.4.2 Conjoined Triangle Point Flexagons;293
12.1.1.3.3;11.4.3 A Conjoined Pentagon Point Flexagon;294
12.1.1.4;11.5 Bundled Odd Edge Flexagons;294
12.1.1.4.1;11.5.1 General Properties;294
12.1.1.4.2;11.5.2 A Five Sector Bundled Triangle Odd Edge Flexagon;296
12.1.1.4.3;11.5.3 The Seven and Six Flexagon;297
12.1.1.5;11.6 Slipagons;298
12.1.1.5.1;11.6.1 General Properties;298
12.1.1.5.2;11.6.2 A Trihexaflexagon Slipagon;298
12.1.1.5.3;11.6.3 A Partial Overlap Silver Even Edge Slipagon;300
12.1.1.6;11.7 Coupled Point Flexagons;302
12.1.1.6.1;11.7.1 General Properties;302
12.1.1.6.2;11.7.2 A Coupled Triangle Point Flexagon;305
12.1.1.6.2.1;11.7.2.1 An Interleaved Conjoined Triangle Point Flexagon;305
12.1.1.6.3;11.7.3 A Coupled Square Point Flexagon;306
12.1.2;References;308
13;162654_1_En_12_Chapter_O.pdf;309
13.1;Chapter 12;309
13.1.1;Miscellaneous Flexagons;309
13.1.1.1;12.1 Introduction;309
13.1.1.2;12.2 Three Sector Odd Flexagons;310
13.1.1.2.1;12.2.1 General Properties;310
13.1.1.2.2;12.2.2 The Three Sector Fundamental Dodecagon Odd Edge Flexagon;310
13.1.1.2.3;12.2.3 A Three Sector Isosceles Triangle Odd Edge Flexagon;311
13.1.1.2.4;12.2.4 A Three Sector Hexagon Odd Skeletal Flexagon;312
13.1.1.3;12.3 Degenerate Odd Edge Flexagons;314
13.1.1.3.1;12.3.1 General Properties;314
13.1.1.3.2;12.3.2 A Degenerate Square Odd Edge Flexagon;314
13.1.1.4;12.4 Alternating Odd Edge Flexagons;315
13.1.1.4.1;12.4.1 General Properties;315
13.1.1.4.2;12.4.2 A Square Alternating Odd Edge Flexagon;316
13.1.1.5;12.5 Flapagons;318
13.1.1.5.1;12.5.1 General Properties;318
13.1.1.5.2;12.5.2 The Fundamental Square Duplex Flapagon;318
13.1.1.5.3;12.5.3 A Square Flapagon–Flexagon Hybrid;319
13.1.1.5.4;12.5.4 The Fundamental Isosceles Triangle Triplex Flapagon;319
13.1.1.6;12.6 Multiplex Edge Flexagons;320
13.1.1.6.1;12.6.1 General Properties;320
13.1.1.6.2;12.6.2 A Square Duplex Edge Flexagon;321
13.1.1.6.3;12.6.3 The Thrice Threefold Flexagon;323
13.1.1.6.3.1;12.6.3.1 Flexing as a Triplex Edge Flexagon;323
13.1.1.6.3.2;12.6.3.2 Transformations and Flexing Using a Threefold Flex;325
13.1.1.6.3.3;12.6.3.3 Transformation and Flexing Using an Asymmetric Fourfold Pinch Flex;328
13.1.1.6.3.4;12.6.3.4 Traversing 3-Cycles by Using Threefold Flexes;330
13.1.1.6.3.5;12.6.3.5 A Trapezoidal Flexagon;330
13.1.1.7;12.7 A Hooke’s Joint Flexagon;331
13.1.2;References;333
14;162654_1_En_Index_Chapter_O.pdf;334