Fuller's Two Volume Synergetics

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Fuller's Two Volume Synergetics

Fuller published a two-volume text called, "Synergetics, the Geometry of Thinking". Read here about this works' treatment of tensegrity and its related concepts. For a general discussion of the Fuller's worldview from which he composed this text, see Synergetics.

Synergetics' Geometrical Innovations

Synergetics claims that all geometric forms known previously as polyhedra can be modelled as tensegrities. As such, Fuller devotes an entire chapter to tensegrity, and tensegrity is discussed throughout the two volume work.

http://www.grunch.net/4dsolutions/kirby.html. Kirby Urner culled from the Synergetics text a list of Fuller's claims of discovery. In Fuller's words:

  • The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity.
  • The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.)
  • The rational identification of number with the hierarchy of all the geometries.
  • The A and B Quanta Modules.
  • The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration.
  • The identification of the nucleus with the vector equilibrium.
  • Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors.
  • Omni-60-degree coordination versus 90-degree coordination.
  • The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical. (See Sec. 251.50)

Tensegrity in the Table of Contents

Below is the table of contents, linked to the online version of Synergetics.

Major table of contents entries

Below are the major headings. Scroll down for a list of all headings in the chapter on tensegrity.

List of figures featuring tensegrity

Below a complete list of figures that accompany the sections on tensegrity. This list appears with thumbnails here: http://www.rwgrayprojects.com/synergetics/findex/fx0700.html

Synergetics table of contents, indented

700.01 Definition: Tensegrity
701.00 Pneumatic Structures
702.00 Geodesics
703.00 Geodesic-Tensegrity Molecular Kinetics of Pneumatic Systems
704.00 Universal Joints
705.00 Simple Curvature: The Barrel
706.00 Compound Curvature: Spherical Cask
706.10 Sphericity
706.20 Three-Way Great Circling
706.30 Fail-Safe Advantages
707.00 Spherical and Triangular Unity
707.01 Complex Unity and Simplex Unity
710.00 Vertexial Connections
711.00 Gravity as a Circumferential Force
711.01 Circumferential Advantage over Radial
711.20 Ratio of Tensors
711.30 Struts as Chords in a Spherical Network
712.00 Clothesline
713.00 Discontinuous Compression
713.01 Subvisible Discontinuity
713.07 Convergence
713.20 Compression Members
713.21 Behavior of Compression Members in Spherical Tensegrity Structures
714.00 Interstabilization of Local Stiffeners
714.01 Local, Discontinuous, Compressional Strut Waves Interstabilizing Two Concentric, Differentially Radiused Tensegrity Spheres
715.00 Locked Kiss
716.00 Complex Continuity and Discontinuity in Tensegrity Structures
716.10 Convergence
717.00 Single- and Double-Bonding in Tensegrity Spheres
720.00 Basic Tensegrity Structures
720.10 Micro-Macro Structural Model
721.00 Stability Requires Six Struts
722.00 Push-Pull Members
723.00 Redundance
724.00 Three and Only Basic Structures
724.10 Tensegrity Octahedron
724.20 Tensegrity Icosahedron
724.30 Six-Strut Tensegrities
725.00 Transformation of Tensegrity Structures
726.00 Six-Pentagonal Tensegrity Sphere
726.01 The Symmetrical, Six-Great-Circle-Planed, Pentagonally Equatored Tensegrity Sphere
730.00 Stabilization of Tension in Tensegrity Columns
730.10 Symmetric Juxtaposition of Tetrahedra
740.00 Tensegrity Masts: Miniaturization
740.10 Positive and Negative
740.20 Miniaturization
740.30 No Solids in Structures
750.00 Unlimited Frequency of Geodesic Tensegrities
750.10 Progressive Subdividing
750.20 Unlimited Subdivisibility of Tensional Components
751.00 Pneumatic Model
760.00 Balloons
761.00 Net
762.00 Paired Swimmers
763.00 Speed and Concentration of Airplanes
764.00 Escape from Compression Structuring
765.00 Snow Mound
766.00 Tensegrity Geodesic Three-Way Grid
770.00 System Turbining in Tensegrity Structures
770.10 Comprehensive System Turbining
770.20 Central-Angle and Surface-Angle Turbining
780.00 Allspace Filling
780.10 Conceptual Definition of Allspace Filling
780.20 Galactic Orientation
780.30 Eternality
780.40 Unitary Conceptuality of Allspace Filling
781.00 Accommodation of Aberration
782.00 Distortion of Vector-Equilibrium Frame
782.10 Accommodation of Aberration: Corollary
782.20 Regularities
782.30 Variability of Spherical Magnitudes
782.40 Isotropic Modular Grid
782.50 Time as Relative Size Experience
783.00 Moebius Strip and Klein Bottle
784.00 Allspace-Filling Tensegrity Arrays
784.10 Basic Allspace Fillers
784.20 Eight-Icosahedra Surround a Nuclear Icosahedron
784.40 Limitless Array of Tensegrity Icosahedra
790.00 Tensegrity Structures
790.10 Definition
790.15 Barrel
790.18 Column
791.00 Cosmic Structuring
792.00 Design
792.10 Universe
792.20 Scenario Universe
792.30 Tension and Compression
792.40 Tidal Complementarities
792.50 Spherical Islands
793.00 Tree Structures
794.00 Geodesic Domes
794.19 Frequency
795.00 Reduction to Practice
795.08 Design Strategies

Links and References

For more information on the author, see Fuller.