1 List of Figures 2 1 Buckminster Fuller (©Phil Haggerty)2 Montréal Expo Dome (©Robert Duchesnay,1988.)1.1 Montréal Expo Dome (©Robert Duchesnay, 1986.)1.2 The Coordinate System of Nature, alias Octet Truss. Thickest lines are elements nearest you and (despite effect of perspective) all members are the same length. Start at bottom left. 1. First-level triangular grid. 2. Tetrahedra, pointing away from you, with octahedra (3) appearing between them. 4. Second-level grid joins tips of tetrahedra. 5. Next array of tetrahedra. 6. Dotted lines show third-level grid. This can be continued indefinitely. Twelve-way vertices (7) in second level are centers of vector equilibrium. (From Hugh Kenner, Bucky: a guided tour of Buckminster Fuller, NY (Morrow) 1973. By permission of the William Hugh Kenner Estate.)1.3 Montréal Expo Dome, 1967 (Estate of R. Buckminster Fuller.)1.4 Cornell University Geoscope (Estate of R. Buckminster Fuller)1.5 Top: Dymaxion Air/Ocean Map (1954). Bottom: Dymaxion Projections re-assembled at South Pole to show British Empire’s ‘One Ocean World’ (R. B. Fuller and S. Sadao. Estate of R. Buckminster Fuller.)2.1 Multi-deck tower apartments; wire-wheel construction (1927.) (Estate of R. Buckminster Fuller.)2.2 4D dwellings—elivery by Zeppelin and North Pole construction (1927.) (Estate of R. Buckminster Fuller.)2.3 Plan of a minimum dymaxion home. (Estate of R. Buckminster Fuller.)2.4 The Wichita House (1945.) (Estate of R. Buckminster Fuller.)2.5 The remains of the Wichita House. (©Robert Duchesnay, 1990.)2.6 Restoring the Dymaxion Dwelling Machine. (©Robert Duchesnay, 1992.)2.7 Fuller and Dwelling Machine model. (Estate of R. Buckminster Fuller.)2.8 Proposed dome over Manhattan. (Estate of R. Buckminster Fuller.)2.9 Baton Rouge Dome. (©Robert Duchesnay, 1990.)3.1 Mumford’s amorous right triangles3.2 Equilateral triangles3.3 3D Isotropic Vector Matrix (Estate of R. Buckminster Fuller.)3.4 The Jitterbug Transformation (R. B. Fuller, Synergetics, NY, 1975)3.5 3.6 Pythagorean tetrakyys3.7 Wesselow, The Growing Magen David (1990)3.8 12-around-1 vector equilibrium configuration of closest-packed spheres3.9 Fuller’s ‘Dymaxion’3.10 ‘‘God geometrizes’’, as Plutarch described Plato’s vision in the Timaeus. Minature from Genesis page, mid-13th Century French Bible, Codex 2554, folio IV, Osterreichische Nationalbibliotetek, Vienna)3.11 The Gothic Master Diagram. (M. Ghyka, The Geometry of Art and Life, New York, 1946)3.12 NaCl (salt), Cuboctahedron and Byzantine Cupola. (Ghyka, Geometry, NY, 1946)3.13 Star-Polyhedra after Leonardo. (Ghyka, Geometry, NY, 1946)3.14 Karachi Mus.3.15 Fuller with early geodesic dome, dymaxion may, tensegrity structure and models derived from his energetic/synergetic geometry; Forest Hills, New York, 1951. (Estate of R. Buckminster)3.16 American Society for Metals Dome, Cleveland. (©Robert Duchesnay, 1990)3.17 Climatron, St Louis. (©Robert Duchesnay, 1990)3.18 Climatron, St Louis. (©Robert Duchesnay, 1990)3.19 The Five Platonic ‘Solids’ (as ‘elements’ in the Timaeus) (Ghyka, Geometry, NY, 1946) 3.20 Fuller3.21 Kepler3.22 Ardagh Chalice (detail)3.23 Śri Yantra3.24 Rose window from Chartres Cathedral3.25 Labyrinth from Chartres Cathedral3.26 Arabic Geometrical Motifs3.27 Spherical Tetrahedron (by S. Eastham; photo ©R. Duchesnay, 1990.)3.28 Triangles of the classical Śri Yantra3.29 Canonical proportions of the Buddha-bodyA.1 Bucky at Black Mountain College with the first great circle models (WHOLES), 1948. (Estate of R. Buckminster Fuller.)A.2 TriangulateA.3 By structure, we mean a self-stabilizing pattern. The triangle is the only self-stabilizing polygon. By structure, we mean omnitriangulated. The triangle is the only structure…Only triangularly structured patterns are regenerative patterns. Triangular structuring is pattern integrity itself. This is what we mean by structure. (¶610.01–3)A.4 Open trianglesA.5 Mated trianglesA.6 Diagonals of a cubeA.7 Volume of a cubeA.8 Structure of a cubeA.9 Simplest self-stabilizing arrangement of spheresA.10 Closest-packed spheres multiplyingA.11 octahedronA.12 terahedronA.13 octahedron-tetrahedron truss (oc-tet truss)A.14 TrussA.15 Three-dimensional model of the fourth dimensionA.16 12 spheres closest-packedA.17 Cube-octahedronA.18 Truncated octahedronA.19 As the circumferentially united and finite great-circle chord vectors of the vector equilibrium cohere the radial vectors, so also does the metaphysical cohere the physical. (¶440.08)A.20 Snow crystals: Vector EquilibrumA.21 Spherical Vector Equilibrum. ©Tom ParkerA.22 (a) icosahedronA.23 (b) CD is to AD as AD is to AB (the smaller is to the larger as the larger is to the whole) AD/CD = Ø AB/AD = ØA.24 (a) Phyllotaxis. If p is the number of turns of the helix and q is the number of stems passed, then p∕q expresses leaf distribution. Both the numerator and the denominator of this fraction are always members of the Fibonacci seriesA.25 (b) Sneezewort (Achillea ptarmica)A.26 (c) Sunflower. The ratio of clockwise to counter-clockwise spirals is always Ø. These interlocking spirals appear wherever we find leaves, kernels, buds or other floral patterns. See, for example, the kernels on a pine cone or the buds on a pineapple. (Η. Ε. Huntley, The Divine Proportion, New York, 1970.)A.27 ‘‘The architect of the future will build imitating Nature, for it is the most rational, long-lasting and economical of methods’’—ntoni Gaudi, cited in the nave of his Sagrada Familia in Barcelona. Photo ©Pere VivasA.28 Ø ratioA.29 (a) A diagram showing a vertical section of the nave, from the Gothic cathedral of Cologne.A.30 (b) The Gothic Standard Plan uses a ten-way division of the circle in equal 36-degree increments, as do the disks you will make for constructing the spherical icosa WHOLE.A.31 Kaiser 145-foot geodesic dome, manufactured in Oakland, California, and erected in 22 hours in Honolulu, Hawaii. At the 22nd hour, the Hawaiian Symphony Orchestra entered; the concert was completed withing 24 hours of the Honolulu landing of the dome’s components. The orchestra conductor pronounced the acoustics as ‘‘the best is his experience’’. (Estate of R. B. Fuller.)A.32 Spherical Icosadodecahedron. ©Tom ParkerA.33 Cube transforms into a sphereA.34 Class m3m; the elements of symmetry, crystallographic axes and a stereogram of the general form. Fig. 303, F. C. Phillips, Introduction to Crystallography, New York (Wiley) 1971, p.163.A.35 Rhombic dodecahedronA.36 Spherical Rhombic Dodecahedron. ©Tom ParkerA.37 Six-great-circle Spherical Octahedron: The doubleness of the octahedron is illustrated by the need for two sets of three great circles to produce its foldable spherical form.A.38 Four primal yantra shapes, based on mathematical equations from the Sanskrit treatise on mathematics, the Ganita Kaumudi (1356)A.39 Archetypal shapes based on the division of a circle.A.40 Chakras (©Janet Α. Evans, from C. W. Leadbeater, The Chakras, Madras/London, 1927.)A.41 JapaneseA.42 ChineseA.43 NordicA.44 BowtiesA.45 American Society for Metals Dome, Cleveland. (©Robert Duchesnay, 1990)A.46 Class 1A.47 Class 2A.48 Buckminster Fullerene: C60— remarkably stable cluster of 60 carbon atoms, formed by vaporising graphite by laser irradiation. Its creators/discoverers suggest this may be the form of carbon carried by diffuse interstellar molecules. (From Nature, Vol 318 No. 6042 pp14–0 Nov. 1995.)A.49 Rhombic TriacontahedronC.1 from S. Eastham, The Radix, Bern (Lang) 1991, p, 133. Document 3
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