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The Geometry of Thinking

Explorations in the energetic-synergetic geometry of Richard Buckminster Fuller

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Greg Frederick, Seattle, Washington

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Introduction and Index

About
Bibliography
Contact
Explorations
Index To Articles
Model Making
More Model Making

Articles

A and B Quanta Modules
A Curious Helical Structure
Anatomy of a Sphere
Areas and Volumes in Triangles and Tetrahedra
Basic Disequilibrium LCD Triangle
Basic Equilibrium LCD Triangle
Blinkers, the Jitterbug, and the “Crystalized” Isotropic Vector Matrix
Calculating the Tetrahedral Volumes of Regular Polyhedra
Calculating the Triangular Areas of Regular Polygons
Categories of Spheres in the Isotropic Vector Matrix: Nuclei, F1 Shells, and “Nuclear Voids”
Close Packing of Icosahedra
Close-Packing of Spheres
Concentric Sphere Shell Growth Rates
Construction Method for the Pyritohedron and Tetrakaidecahedron of the Weaire-Phelan Structure
Cube
Diagonal of the Icosahedron
Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
Dual Nature of the Tetrahedron
Equivalence of Tetrahedron Edge Length and Structural Quanta per Volume of its Inscribed Polyhedra
Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
General Unit Conversions
Geodesics
Golden Ratio
Great Circle Bow-Ties of the Icosahedron
Great Circle Bow-Ties of the VE
Great Circles: Spherical Polyhedra Disclosed by Great Circles of the Icosahedron
Great Circles: Spherical Polyhedra Disclosed by Great Circles of the VE
Great Circles: The 25 Great Circles of the Vector Equilibrium (VE)
Great Circles: The 31 Great Circles of the Icosahedron
Icosahedron
Icosahedron Inside Octahedron
Icosahedron Phases of the Jitterbug
Inter-Geared Mobilities of the De-Nucleated Vector Equilibrium
Inter-Sphere Connections via the 25 Great Circles of the VE
Isotropic Vector Matrix
Isotropic Vector Matrix as Transverse Waves
Jessen Orthogonal Icosahedron and Tensor Equilibrium
Jitterbug
Jitterbug Animations with Spheres
Kelvin Truncated Octahedron
Minimum All-Space-Filling Tetrahedron: “MITE”
Multiplication and Merger of Spheres in the Jitterbug
Octahedron
Operational Geometry
Pentagonal Dodecahedron
Pi and the Synergetics Constants
Polyhedra From Polygonal Strips
Polyhedra With Whole Number Volumes
Pyritohedron Dimensions and Whole-Number Volume
Quanta Module Constructions of the Rhombic Dodecahedron
Rhombic Dodecahedron
Rhombic Triacontahedron
S Quanta Module*
Seven Axes of Symmetry
Space-Filling Polyhedra as Close-Packed Spheres
Spaces and Spheres (Redux)
Spheres and Spaces
T and E Quanta Modules
Tensegrity
Tensegrity Equilibrium and Vector Equilibrium
Tensegrity Sphere Equations
Tetrahedron
Tetrahelix
Tetrakaidecahedron and Pyritohedron
Tetrakaidecahedron Dimensions and Whole Number Volume
The 25 Great Circles of the VE (new illustrations)
The 31 Great Circles of the Icosahedron (new illustrations)
The Jessen Orthogonal Icosahedron in the Isotropic Vector Matrix
The Polar Pump Model of the Jitterbug
There’s Just One Way to Stack Cannonballs
Topological Abundance Formulas
Twoness: The Multiplicative and Additive Two
Unique Properties of the Tetrahedron
Vector Equilibrium and the “VE”

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