A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller (1986)

1. Return to Modelability.- From Geometry to Geodesics: A Personal Perspective.- Operational Mathematics.- Experimental Evidence.- Coordinate System.- Universe.- Generalized Principles.- Return to Modelability.- 2. The Irrationality of Nature Isn't Using Pi.- Finite Accounting System.- Which Way Is Up?.- Visual Literacy.- Peaceful Coexistence.- 3. Systems and Synergy.- Conceptual and Real Systems.- Limits of Resolution as Part of the Whole-Systems Approach.- Synergy.- 4. Tools of the Trade.- Plato's Discovery.- Triangles.- Squares.- Pentagons.- A Limited Family.- Euler's Law.- Duality.- Truncation and Stellation.- An Experiment.- Intertransformability.- Symmetry.- 5. Structure and Pattern Integrity.- Structure.- 6. Angular Topology.- Frequency and Size.- Units of Measurement.- Time and Repetition: Frequency versus Continuum.- Topology and Vectors.- Vector Polyhedra.- Dimension.- Size.- Planes of Symmetry.- Other Applications of Dimension.- Angular Topology.- Angular Takeout: An Example.- Angle Types.- 7. Vector Equilibrium.- Nature's Own Geometry.- Spatial Considerations.- Planar Equilibrium.- Cuboctahedron as Vector Equilibrium.- VE: Results.- Degrees of Freedom.- 8. Tales Told by the Spheres: Closest Packing.- Equilibrium: Equalization of Distances.- Symmetry versus Specificity of Form.- Organization of Identical Units.- New Level of Focus.- Background: Closepacking.- Planes of Symmetry.- Fuller Observations.- Tetrahedra.- Vector Equilibrium.- Frequency.- Icosahedron.- Further Discoveries: Nests.- Interprecessing.- A Final Philosophical Note.- 9. Isotropic Vector Matrix.- A Quick Comparison: Synergetics Accounting.- Cells: Inherent A Complete Picture.- Angles.- Locating New Polyhedral Systems.- Duality and the IVM.- Angles.- Polyhedra.- Domain.- Framework of Possibility.- Invention: Octet Truss.- 10. Multiplication by Division: In Search of Cosmic Hierarchy.- Volume.- Results: Volume Ratios.- Shape Comparisons: Qualities of Space.- Volume: Direct Comparison.- Multiplication by Division.- Tetrahedron as Starting Point.- Cube.- Vector Equilibrium.- Rhombic Dodecahedron.- Multiplication by Division.- Cosmic Hierarchy (of Nuclear Event Patternings).- Volume Reconsidered.- 11. Jitterbug.- Folding a Polyhedron.- Volume and Phase Changes.- Icosahedron.- Single Layer versus IVM.- Trans-Universe versus Locally Operative.- Fives.- S-Modules.- Icosahedron and Rhombic Dodecahedron.- Pentagonal Dodecahedron.- Four Dimensions.- Complex of Jitterbugs.- Other Dynamic Models.- Topology and Phase.- 12. Filling: New Types of Packing Crates.- Plane Tessellations.- Filling Space.- Complementarity.- Other Space Fillers.- The Search Continues.- The Dual Perspective.- Duality and Domain in Sphere Packing.- Truncated Octahedron.- Two to One: A Review.- 13. The Heart of the Matter: A- and B-Quanta Modules.- A-Quanta Modules.- B-Quanta Modules.- Energy Characteristics.- Mite.- Mirrors.- Cubes into Mites.- Rhombic Dodecahedra.- Coupler.- Volume and Energy.- Review: All-Space Fillers.- 14. Cosmic Railroad Tracks: Great Circles.- Why Are We Talking About Spheres?.- New Classification System.- Great-Circle Patterns.- Least Common Denominator.- LCD: Intertransformability.- LCD of 31 Great Circles.- VE's 25 Great Circles.- Operational Mathematics.- Conservation of Angle.- Foldable Systems.- Energy Paths.- Gas Molecules.- Great-Circle Railroad Tracks of Energy.- Icosahedron as Local Shunting Circuit.- Inventory: Seven Unique Cosmic Axes of Symmetry.- Excess of One.- 15. From Geodesic to Tensegrity: The Invisible Made Visible.- Theory Behind Geodesic Structures: Summary.- Geodesic in Nature.- Geodesic Domes: Variables.- Tensegrity.- Example.- New Concept of Construction.- Modeling the Invisible.- Tensegrity Polyhedra.- Pneumatics.- Case in Point: Donald Ingber.- 16. Design Science.- Comprehensive Anticipatory Science.- Comprehensive... .- ... Anticipatory... .- Dymaxion Map.- Suspended Storage Systems.- More with Less.- Appendices.- A. Trigonometric Calculations.- B. Volume Calculations for Three Prime Structural Systems.- C. Sources of Additional Information.- D. Special Properties of the Tetrahedron.- E. Glossary.- Notes.