Fuller's Two Volume Synergetics

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.

• 700.00 TENSEGRITY
• 720.00 Basic Tensegrity Structures
• 730.00 Stabilization of Tension in Tensegrity Columns
• 740.00 Tensegrity Masts: Miniaturization
• 750.00 Unlimited Frequency of Geodesic Tensegrities
• 760.00 Balloons
• 770.00 System Turbining in Tensegrity Structures
• 780.00 Allspace Filling
• 790.00 Tensegrity Structures

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

• Figure 705.01
• Figure 705.02
• Figure 712.01
• Figure 716.01
• Figure 717.01
• Figure 724.10
• Figure 724.30
• Figure 725.02
• Figure 730.11
• Figure 730.12
• Figure 740.21
• Figure 761.02
• Figure 762.01
• Figure 765.02
• Figure 770.11
• Figure 770.21
• Figure 784.20
• Figure 784.30
• Figure 784.41
• Figure 791.01

Synergetics table of contents, indented

700.00 TENSEGRITY

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.