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Geodesic Math and How to Use It
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Contents
What This Book Is
I Tensegrity
1 Weight vs. Tension
1.1 Appendix to Chapter 1: Tensegrity Prisms
2 Spherical Tensegrities
2.1 Equilibrium
2.2 Elasticity Multiplication
3 Complex Spherical Tensegrities
3.1 Great Circle Tensegrities
3.2 Dip-Angle Calculations
3.3 Calculation of Remaining Dimensions
3.4 Appendix to Chapter 3: Derivation of Tensegrity-Sphere Equations
4 Tendon System Minima
4.1 Six-strut Tendon Minima
5 Geodesic Subdivision
6 Rigid Tensegrities
6.1 Numerical Example
II Geodesics
7 Great Circles
7.1 Great-Circle Systems
7.2 Octahedral and Tetrahedral Great Circles
8 Symmetry Systems
8.1 Envelope Contours
9 The Spherical-Coordinate System
10 Breakdown Systems
10.1 Class I (Alternate)
10.2 Class II (Triacon)
10.3 Which Class?
10.4 Which Frequency?
11 Choosing a Polyhedron
11.1 Other Criteria
12 Using the Tables
12.1 Planning the Work: Class I
12.2 Accuracy
12.3 Class II
12.4 Appendix To Chapter 12: Derivation of the Coordinates
13 Ellipses and Superellipses
13.1 Octahedral Ellipsoids
13.2 Modifying Coordinates
13.3 Superspheroids
13.4 Varying Two Radii
13.5 Free Forms
14 Truncations
14.1 Truncation by Rotation
14.2 Novel Truncation Planes
14.3 Zenith Altitude and Floor Radius
15 An Advanced Problem
15.1 Quartering the Icosa
15.2 Writing the Coordinates
15.3 Rotating the Coordinate System
15.4 Tabulating the Radii
15.5 Chord Factors
15.6 Truncation
16 Space Frames
16.1 Diamond Patterns
16.2 Trussed Frames
17 About Angles
17.1 Axial Angles
17.2 Face Angles
17.3 Dihedral Angles
III Data
18 Class I Octahedral Coordinates
19 Class II Method 1 Octahedral Coordinates
20 Class I Method 1 Icosahedral Coordinates
21 Class II Method 1 Icosahedral Coordinates
22 Tetrahedral Coordinates
23 Class II Method 3 Coordinates and Chord Factors
Appendices
Appendix I: Writing Class II Method 3 Coordinates
Appendix II: Calculator Routines
Appendix III: HP-65 Programs
List of Figures
List of Tables
Bibliography
Index
Index
List of Figures
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.1
2.2
3.1
3.2
3.3
3.4
3.5
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