Multimodular Origami Polyhedra Archimedeans,

Explore the link between paperfolding and mathematics with this unique, well-illutrated guide to creating a world of multifaceted wonders that draws on elements of crystallography. Photographs, diagrams, and charts show how to apply mathematical principles to the origami waterbomb base to create geodesic forms. Detailed instructions, clear diagrams.

Introduction

1

(2)

Background Material

3

(4)

Archimedean Solids

4

(1)

Duality

4

(1)

Gyroscoped Archimedeans

4

(1)

Gyroscope Modules

5

(1)

Buckyballs

5

(1)

The Eggs

6

(1)

Gallery of Polyhedra

7

(32)

The Egg and the Gyroscoped Egg

8

(1)

Archimedeans, Catalans, and Gyroscoped Archimedeans

9

(14)

Gyroscoped Truncated Tetrahedron

10

(1)

Gyroscoped Cuboctahedron

11

(1)

Gyroscoped Truncated Octahedron

12

(1)

Gyroscoped Truncated Cube

13

(1)

Gyroscoped Rhombicuboctahedron

14

(1)

Gyroscoped Truncated Cuboctahedron

15

(1)

Gyroscoped Snub Cube

16

(1)

Gyroscoped Icosidodecahedron

17

(1)

Gyroscoped Truncated Icosahedron

18

(1)

Gyroscoped Truncated Dodecahedron

19

(1)

Gyroscoped Rhombicosidodecahedron

20

(1)

Gyroscoped Truncated Icosidodecahedron

21

(1)

Gyroscoped Snub Dodecahedron

22

(1)

Seeds for Growing Buckyballs, Buckyballs, Hypothetical Buckyballs, and Their Gyroscoped Forms

23

(16)

3-1-1

24

(1)

3-3-2

25

(1)

3-3-1

26

(1)

3-7-2

27

(1)

3-7-1

28

(1)

4-1-1

29

(1)

4-3-2

30

(1)

4-3-1

31

(1)

4-7-2

32

(1)

4-7-1

33

(1)

5-1-1

34

(1)

5-3-2

35

(1)

5-3-1

36

(1)

5-7-2

37

(1)

5-7-1

38

(1)

Model Construction

39

(10)

Model Selection

40

(1)

Module Selection

40

(1)

Module Sizing

40

(2)

Nets as Guides: Naming System for Polyhedra

42

(1)

Model Assembly

43

(5)

Four-Sided Display Stand from a Pentagon Waterbomb Base

48

(1)

Polygon Construction

49

(11)

Symbols

50

(1)

How To Make an Equilateral Triangle

51

(2)

From a Square

51

(1)

From a Tesselation

51

(1)

From a Strip

52

(1)

How to Make a Pentagon

53

(4)

From a Square

53

(1)

Pentagon Template 1: From a Square

54

(1)

Pentagon Template 2

55

(2)

How to Make a Hexagon

57

(1)

How to Make an Octagon

58

(1)

How to Make a Decagon

59

(1)

Module Construction From Polygons

60

(15)

Basic Tab and Pocket Lock

61

(10)

One-Piece Triangle Module

61

(1)

One-Piece Square Module

62

(1)

Simplified Pentagon Module

63

(1)

Simplified Hexagon Module

64

(2)

How to Petal-Fold a Squashed Vane

66

(1)

Octagon Module

67

(3)

Decagon Module: Abbreviated Instructions

70

(1)

Large Models: Hexagon/Pentagon Pocket and Connectors

71

(4)

Expanded Pentagon Spike Ball Module

71

(1)

Expanded Hexagon Spike Ball Module

72

(1)

Locking Connector for Pentagon and Hexagon Spike Ball Modules

73

(1)

Locking Expanded Spike Ball Modules

74

(1)

References and Acknowledgments

75

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Multimodular Origami Polyhedra Archimedeans, Buckyballs and Duality

Summary

Table of Contents

Supplemental Materials