4 TENSILE INTEGRITY IN ARCHITECTURE
2NOWHERE is Fuller’s comprehensive approach more vividly portrayed for all to see and comprehend than in the field of architecture. In this instance, what exactly, is meant when we say, ‘‘comprehensive’’? Well, to begin with, Fuller does not at first think abstractly of architecture by itself. That would be yielding to a restraint imposed by the chains of old thought which generated the notion that architecture is something which can be placed off in a compartment by itself. Rather he thinks of man and his environment as he ponders the broad range of man’s experience in housing himself against the elements.1 This is translated into everyday language as (a) selection and use of materials, (b) ascertainment of the manner in which the selected materials can be used to greatest economic advantage, (c) study of the feasibility of prefabricating components of the ultimate structure (or, as with some of Fuller’s architecture, prefabricating the entire structure), (d) analysis of the logistics of transporting the materials, components or finished structure to the erecting site. This is not the end of the list, nor is there necessarily any such formal outline in Fuller’s mind, his being the more comprehensive unstyled contemplation of the whole of man’s environment in its relation to the ‘‘architectural’’ problem at hand. It is just that his intellect, free from inhibition, is touching and sorting multiple facets of man’s ‘‘sensed and translated experience’’ as it permits itself to reach, intuitively, new crystallization of experience into a more perfect unity. The crystal of thought so formed will be fresh and sparkling in its purity of conception within a frame of reference that is at once mathematical, dynamic, and conscious of Universe as a whole. That crystal in the present instance becomes the ‘‘geodesic’’ dome; a structure capable of enclosing most space per ounce of material used, and which utilizes synergetically the ultimate quantum of available tensile strength properties of that material. Through millenniums of history, man, with endless persistence and inexhaustible patience, has piled stone on stone, log on log, beam on column. In the process, he selected materials that would best resist crushing, for his plan was to carry loads in compression. As an exception to the rule stood the tepees and other tent forms of die nomadic tribes of Indians and Arabs. Tents, however, were not translatable to the needs of society generally, and the lesson that they might have taught in the use of tensile strength of lighter weight materials never reached beyond field camps for the military and the circus tent. The Iron Age brought the steel girder, an assembly of parts some of which were placed in tension, but the majority of which still relied on the ancient scheme of using the compressive, or columnar, strength of the girder elements. Then there was the suspension bridge whose cables utilized the tensile properties of the steel wire from which the cables were spun. But in houses and buildings, when tensioned elements were used at all, these were only incidental to the great scheme of a piled-up structure, standing as a ponderous reminder of the pyramids of Egypt. Compression was still King of the forces. This, notwithstanding the fact that the technologies of metallurgy, glass fibre making, and of chemistry in plastics, had developed significant improvement in the tensile properties of materials, whereas comparatively little could be done to increase strength in compression. Fuller observed, ‘‘If we have better metallurgical alloys, we can make longer and longer tension members with less and less section—apparently ad infinitum, but not longer and thinner compression columns, ad infinitum.’’
4 Such was the setting of the stage when the scene of building history shifted, and there stood Fuller’s ‘‘geodesic’’ dome, made of mind and geometry. It was an extremely lightweight, spidery structure whose parts interacted with one another in a most remarkable tensile network. Previously, Fuller had invented a round house supported from a central mast. This, too, had been designed with the objective of making better use of the tensile strength of building materials. Concerning this unusual form of house, Fuller was asked, ‘‘Why do you build a house that is round?’’ His quick response was, ‘‘Why do you build one that is square?’’ Then, answering his own question, ‘‘Originally, a log house came out square because the logs were straight, making the sides of the house straight. An Eskimo did not experience this limitation, and perhaps intuitively since nature made men’s skulls spheroidal rather than cubical, he made his igloo in the form of a dome uniquely suited to his needs, being easy to heat efficiently, and providing the greatest amount of living volume per block of ice used in its construction. So now,’’ Fuller explained patiently, ‘‘we have building materials which are admirably suited to the erection of structures without any limitation as to their form. This affords more efficiently and to greater us the opportunity of building functional advantage.’’
5 Above all, Fuller had been seeking a way of using man’s material building resources to best possible advantage. The greatest unused potential of the properties of available materials lay in their tensile strengths. To his mind, comprehending at first only the totality of the problem, and unfettered to any preconceived notions of form or structuring, the assignment was exciting in the freedom of choice he afforded himself. No idea of doing the unconventional, but just the innate urge to find the ‘‘minimum system for enclosing space,’’ regardless of whether or not it be conventional. He was not going to be conventional for the sake of conforming to what was accepted, but neither was he concerned with any need to depart from the norm. Perhaps, as with atonal music, he was only being ‘‘a-conventional.’’ He simply had to find the one best answer, the ultimate solution.
6 This was a matter which concerned conservation of the world’s material resources, and was not to be taken lightly. It was an inseparable part of his philosophy, which he formulated in these carefully chosen words: ‘‘The possibility of the good life for any man depends upon the possibility of realizing it for all men. And this is a function of society’s ability to turn the energies of the universe to human advantage.’’ In the new architecture of geodesics, human advantage was to be sought through maximum utilization of tensile force, or, as he was wont to express it, through maximum ‘‘tensile integrity’’ in architecture. In his classroom shorthand, ‘‘Tensegrity.’’
7 Buckminster Fuller’s geodesic dome patent,2 entitled simply, ‘‘Building Construction,’’ is a remarkable document as patents go. To begin with, the fundamental nature of the inventive concept had at once created a new language of its own. As with the radio and the telephone, the geodesic dome was a pioneer, and a new dictionary was needed to name it and to designate its new parts. The patent includes a section entitled, ‘‘Definition of Terms,’’ these being terms which have come to be used in the new art of geodesic construction with special connotation—terms such as ‘‘icosacap,’’ ‘‘three- way great circle grid,’’ ‘‘modularly divided,’’ and ‘‘frequency.’’ The structure is described as being spherical, or having the form of a portion of a sphere; or, it can be polygonal, a ‘‘faceted’’ sphere. The individual structural elements are so arranged as to be aligned with great circles of a sphere. Seven years earlier, Fuller had discovered how, in the field of cartography, surprising advantages accrued through the use of ‘‘great circles.’’ So here we have another indication of the comprehensive nature of Fuller’s inventorship, for it finds a least common denominator for inventions in map-making and architecture, just as his discoveries in the field of mathematics found congruence in nuclear physics and molecular biology. Fuller has suggested the possibility that the ultimate in comprehensive discovery could some day reduce ‘‘inventing’’ to a purely mathematical process. Certain it is that the more man comprehends, the greater is the range of new ideas that appear to him to be obvious, whereas in the patenting of inventions, the law says that only the unobvious is patentable.
9 To pursue Fuller’s suggestion concerning the application of mathematics to inventing by considering what may be a case in point, we might well investigate what influence Fuller’s comprehensive discovery of the new geometry could have had in leading to his invention of the geodesic dome. We have noticed that early in his presentation of energetic/synergetic geometry, Fuller stressed the point that a triangle drawn on the Earth’s surface is actually a spherical triangle bounded by great circle arcs. And, a moment ago, we learned that in describing the geodesic dome, the inventor explained that its structural elements are aligned with great circles of a sphere. Hence we see that the ‘‘great circles’’ of the geometry reappeared in the structuring of the geodesic dome. If we were to continue our investigation into a deeper stratum of analysis, we would discover another common base between the geometry and geodesics, for it turns out that in the geodesic dome, Fuller has called upon that ‘‘first identifiable system of Universe,’’ the tetrahedron, and its stabilizing vector system.
10 Thinking first only of the great circles as a least common denominator of geometry and dome, we may ask, ‘‘How would Fuller arrange these circles?’’ The patent document states with definitive geometry that the circles are to lie in planes which contain the vertexes of a polyhedron. So much for definition with the range of acceptable Patent Office semantics. The fact is that Fuller did not ‘‘arrange’’ the circles in the sense that one would arrange beams in a conventional building. He permitted nature, or nature’s geometry, to do it. Besides that most remarkable tetrahedron with its stabilizing vector system, there was also the icosahedron complex which was capable of bringing that vector system into play for a spherical breakdown useful in dome architecture.
11 By this time it must be reasonably clear that the pattern of inventive thought which created the geodesic dome was strongly influenced by the compatible inventive pattern which brought energetic/synergetic geometry into being. We need not decide the validity of Fuller’s thought that the ultimate in comprehensive discovery could one day reduce all inventing to a mathematical process. Perhaps that could happen only in the case of ‘‘genius’’ inventing, having a depth of perceptive analysis such as Fuller’s.
12 Fuller’s genius flourished in the climate of his ability to strike from mental consciousness every shred of prior analysis, so as in effect to create a vacuum into which might flow the perceptiveness of new natural thought. The observed phenomena of nature can then create greater purity and depth of perception—an intuitive awareness akin to what Fuller has described as ‘‘the extraordinary moments of purely poetical lucidities of man.’’ It must almost certainly have been just such an extraordinary moment which brought to Fuller*s mind the concept of how the geometry that was ‘‘Nature’s own,’’ would arrange the great circles to best advantage in architecture. The icosahedron, expressing that geometry, exploded onto the surface of a sphere, did the job that the patent described in definitive terms as ‘‘great circles which contain the vertexes of a polyhedron.’’
13 The icosahedron is a figure having twenty equal, equilateral faces. Uniquely, the icosahedron has an inversion, or alter ego, in the dodecahedron, a figure which has twelve equal, equilateral faces. Whichever is considered as the starting point in the geometry of solids, the resulting pattern of great circles comes out the same. This is a third example of the two-ness of the universe as observed by Fuller in the cases of the convex-concave spherical triangle and of the tetrahedral ‘‘hour-glass.’’
14 It is quite essential that we notice these mathematical probes in order to comprehend the scope of Fuller’s thought pattern. We then can perceive in some measure the dynamism of a mind that moves in ever accelerating curve toward infinitude of understanding in which ‘‘the whole of man’s sensed and translated experience’’ finds congruence—in which mathematics, physics, chemistry, and biology will one day be seen only as parts of a greater whole which, responding to unifying force, reveals an exquisite underlying pattern of the motion that is life itself. Advancing far through the distances to that day of great understanding, Fuller has already identified a system which links together geometry, cartography, virus structuring and geodesic architecture.
15 The architect’s great circles, defined by intersections with a sphere of planes passing through the vertexes of those peculiar polyhedrons, ‘‘icosa’’ and ‘‘dodeca,’’ create a sophisticated relationship. Used as the patterning of geodesic domes, and superimposing what geodesic designers call ‘‘three-way gridding,’’ the circles and grids produce a uniformity in overall pattern that is at once apparent even to an unpracticed eye. The visual manifestations of the pattern are many and surprisingly varied. In one there is a total complex of equilateral triangles. In another, diamonds. In a third, hexagons, but revealing a number of pentagons as well which, upon careful examination, are found to occur at each of the twelve vertexes of the originating icosahedron. This demonstrates that the integrity of the icosa has been preserved.
16 What is the true worth of these distinctive patterns in terms of structural advantages, it is logical to ask. Answer: a building erected according to such a pattern is exceptionally strong and possesses optimum stability, being inherently capable of distributing stresses from here to there or, more accurately, from any point to the structure as a whole. When a force is applied so that its loading is concentrated at a single point, the tendency to deform the structure at that point will be resisted by the total complex of the framework—much as a rubber ball will absorb the impact of its bounce.
17 A further perspective is gained by comparing geodesic construction with that of the familiar form of dome in which supporting arches converge to intersect one another at the apex. Imagining the apex to be one of the poles of a world globe, the sides of the arches will appear as the meridians of longitude. Through the arches, forces or loading applied to this form of dome are transmitted to a single point of congruence at the apex, or ‘‘pole,’’ where they are concentrated, rather than distributed. This, then, is ‘‘polarized’’ structuring. Geodesics, the antithesis of this, is non-polarized and force-distributing.
18 To some eyes, the strangeness of geodesic structuring sets it rather apart from practical building norms, taking as the norm the more conventional forms of past and present. This means of course the familiar vertically-walled building and its variations. Of these, Fuller states, ‘‘They are buildings which want to fall down, and so must be braced and gusseted against doing so.’’ And adds, ‘‘Whereas geodesic domes just naturally want to stand up.’’ It is a tribute to the soundness of geodesic design and engineering that unconventionality of form and construction has not prevented its use and acclaim throughout the world for many purposes less well served before. Licensed to some eighty manufacturers, the geodesic dome has been constructed of steel, aluminum, magnesium, wood, plastics—even of paperboard. Light, compact as capsuled for shipment, the domes have been airlifted to building sites otherwise inaccessible, as at polar bases and even in the mountain fastnesses of the Himalayas. Size of geodesic buildings seems virtually without any limitation. They have been built in sizes big enough to cover a football field, and designs have been engineered for structures that can provide weather breaks for entire cities. Even an abbreviated fist of geodesic projects completed would be less than representative without mention of dome houses for earthquake relief, weather breaks for electronic defense warning systems, domes for trade fairs around the world, United States Marine Corps shelters and the United States Pavilion at the World’s Fair at Montreal, Canada. It seems a portent for the future that there is a manufacturer of educational geodesic building sets from which today’s children will be able to learn about geodesic geometry by putting together icosa-form structures.
19 Architectural students throughout the United States now know the language of geodesics, as do others in Africa, India and Japan. Knowing this, all should want to understand something about this fundamentally new concept in architecture. More importantly, it should be understood for what it truly is, a comprehensive answer to the question: How can the world utilize to its greatest commonweal the prodigious strength of materials in tension? What geodesics comes down to is:
20 The invention of a structure that uses tension to higher advantage. A structure of greater tensile integrity. In a new word, ‘‘Tensegrity.’’
21 THE United States patent on geodesic construction was granted in 1954. By the end of 1955, the dynamic concepts of geodesics and tensegrity were beginning to stir the minds of engineers and architects. In that brief moment of history, eight corporations had sought and obtained licenses under the patent and were busy manufacturing geodesic structures in wood, steel, aluminum and magnesium. The United States Marine Corps had discovered that geodesics opened the way to a whole new logistics for swift movement of troops and supplies, and was ordering production of geodesic shelters which could be air-lifted to advance bases. These were put together as a framework of magnesium struts supporting skins of tensioned nylon plastic in uncompromising acceptance of the fundamentals of tensile integrity.
22 But the questing mind of Buckminster Fuller at this moment of acceptance did not pause in contemplation of his personally engineered triumph for tensile architecture, for it was busy racing toward the forever of the future. Unable to accept magnesium and nylon as necessarily being the ultimate in rebellion against man’s self-imposed burden of stone and steel, the eye of his mind plummeted on in its search for a surpassing perfection. What even greater use might be made of the energy of the universe for benefit of man? What material could be fighter than the lightest metal skinned with a froth of nylon? Cardboard? ‘‘Ridiculous,’’ you say? To Fuller, no answer was to be rejected by hitching it to the ball and chain of castigation. No, cardboard might do the job. Paper on edge, as a column would support nothing heavier than a fly. But it does have tearing strength—tensile strength.
23 Thus was born another invention concerned with the fundamental philosophy of turning the energy of the universe to greatest human advantage. And so, almost before the signatures of Fuller’s eight pioneering manufacturers were dry on their geodesic licenses, there came into being at the advent of the new year 1955, an application to patent the ‘‘paper’’ building. This was a structure which, in correct appraisal, could only be described as being made of cellulose and the geometry of geodesics plus a still newer increment of tensile integrity. Four years later, the patent granted on that application gave official recognition to the newer increment by the allowance of claims which define tensile stressing of paperboard components of a geodesic dome. Because the geodesic dome itself is a tension structure possessing what is known as tensile integrity, the use in that structure of a component which has been stressed in tension, produces an exquisite compounding of tensile force patterns. In Fuller’s starkly revealing semantics, this is explained as a tensile integrity of both structured component and structured dome.
24 To form an idea of the nature of this force complex, the first step will be to visualize how the individual structured component is made and stressed. In the beginning, there is only a simple rectangular piece of paperboard. It is scored to create two fold lines lengthwise of the rectangle, and two crosswise, then bent first round the lengthwise folds into a tube having three flat walls—a tube of triangular section. The tube is then bent around its crosswise folds into a triangular picture frame. Gores cut at the crosswise folds allow the frame to take its intended shape without rupturing. At this point there has been formed a triangular frame each of whose three sides is a three-faced tube, that is, triangular in cross section.
25 Now appears the new increment of tensioning. Its dynamics will not be visible, but can be explained:
2627When the tube is being folded into a triangular frame, the material of the tube is ‘‘crowded’’ at the comers of the frame. This is a function of the special design of the gores and flaps adjacent the crosswise folds. The intentional crowding of the material at the comers of the frame has the result of applying tension to the outside of the frame. It is this tension which affords tensile integrity of the structured component of the dome in which it will become a part of the inherent geodesic stress pattern.
28 Now as the number of such tensile components is multiplied, while adhering to integrity of the geometry of geodesics as one component may vary undiscemably from another according to what is known as the frequency of the particular dome design selected, there will have been created all of the basic structural elements needed to construct a building that will inherently provide what Fuller encapsulates in his phrase, ‘‘tensile integrity of both structured component and structured dome.’’
29 By coating the paperboard with a plastic before the rectangular pieces are tension-folded, the tensile aspect of the building is further increased by reason of the utilization of the tensile strength of a plastic film. The result is a building which in a very real sense derives its strength from ‘‘paper and paint,’’ plus that priceless new ingredient, tensile integrity compounded.
30 When the family of interrelated tensioned triangles is brought together in its geodesic geometry of a completed dome, two events occur, one that can be seen, another that cannot. The first is the visible mating of the several members of the family into the characteristic beauty of geodesic pattern. The second is the invisible mating of tensile integrities, and it is the event of greater significance to man in his strivings to afford himself more of the blessings of nature.
31 At almost the same moment that Fuller was readying his disclosure of this invention for presentation to the Patent Office, the dome of paper and geometry was being shown in Milan, where, at the Triennale Exhibition, it won for the United States the grand prize in architecture.
32 The patent was granted.3 AS Fuller’s new art of geodesics brought a forward gain for all men through optimum use of tensile force to conserve material, so also did it reduce man’s labor in transport and building, for none of the material that was saved needed to be handled. But there was still more to it than that. In the beauty of its simplicity, the geodesic structure had fewer parts, and could be built within a tiny fraction of the time needed for erection of more conventional structures. Hence it could sooner be made ready for occupancy and use. Here was another dividend of the comprehensive approach: Time, the fourth dimension of geodesics. The equation becomes
3435Tensile integrity = conservation of material resources + conservation of time.
36 The sum of Fuller’s success in geodesics thus can be expressed as a four-dimensional ‘‘ability of society to turn the energies of the universe to human advantage.’’
37 In 1956, the United States Information Agency decided that it would like to have a pavilion at the international trade fair in Kabul, Afghanistan. Kabul was not accessible by railroad or highway. The problem was how to transport and erect a big enough building of any kind in such an inaccessible spot. Air transport could be the only solution, but sending a building by air would be a large order!
38 Sixty days later and the building wished for was there in faraway Kabul, erected and ready for use as the United States pavilion, an 8,000 square foot geodesic dome of 117 feet clear-span diameter. Within that sixty days, the pavilion had been conceived, its spherical geometry calculated, its drawings made, its components manufactured, assembled, tested, disassembled and packaged for shipment, loaded into a single DC-4 cargo plane, flown to a building site halfway round the world, and erected. The erection time was twenty-four hours.
39 A photograph of the Kabul dome appears in the United States patent that was granted to cover this further advance in the geodesic art.4 Fuller had discovered that if he combined a geodesic frame with a geodesically patterned plastic skin, these two structural complexes would interact one with the other in a very special way. The secret was to make the two structures, frame and skin, ‘‘conform in structure, pattern or behavior to a mutual three way great circle synergy.’’ He described the effect in these words:
4142[It] gives a new and synergetic stress distribution-synergetic in the sense that the behavior of the skin under stress is unpredicted by its several parts, and there is imparted to the structure a strength beyond that which would be calculated using accepted values of strengths of materials and usual methods of stress analysis and computation.
43 The skin could be made of either flexible or rigid materials so that in one sense it could be an outwardly framed tent, or in another a domed building, of compound geodesic stress characteristics.
44 If we wish to comprehend more firmly the course of the inventor’s stream of thought, and appreciate its motion, we will notice the vitality of his recurrent emphasis on dynamics. Never just materials in static concept, but forces in a more abstract sense. It seems almost to be an inversion of the ordinary engineering that thinks of forces as being applied to materials. With Fuller, it is the force that is first in contemplation, while the material is secondary. Too, we will notice a pervasive understanding of the reality of synergy as opposed to the unreality of ordinary mathematics. As with the ‘‘inadvertent appearance of a fourth triangle’’ in the example given (supra, page 26) which made ‘‘1 + 2 = 4,’’ we now have the synergetic effect of two great circle structures interacting one with the other. Additionally, we will notice that in all his inventions, the map, the geodesic structures, and in others to be discussed, Fullers thoughts never lose touch with the mathematics of his own energetic and synergetic geometry, nor with a deep philosophical awareness of the existence of an exquisite underlying pattern in the entire universe of man’s experience.
45 It can scarcely be doubted that it is these several ingredients of Fuller’s comprehensive outlook which bring to his inventions that fundamental character which today are called ‘‘breakthroughs.’’ They are of the kind which reveal force patterns of universal application in what we have been accustomed to think of as so many different fields of the sciences. In summary, Fuller’s thought stream is characterized by: (a) emphasis on dynamics, (b) grasp of synergy as true reality, (c) link to energetic/synergetic geometry, and (d) awareness of underlying pattern in the universe.
46 IT was now 1956, second year after granting of the first patent in geodesics. Government and business were giving evidence of a growing need for geodesics and tensegrity. That year the roll of industrial licensees under Fuller’s patent rights climbed to thirty-one, including such diverse interests as Magnesium Products of Milwaukee, Lunn Laminates, Inc., Domestic Film Products Corp., Container Corporation of America, The Firestone Tire and Rubber Company, and Kaiser Aluminum & Chemical, Inc.
47 Initial impetus was supplied when the United States Marine Corps demonstrated the feasibility of moving lightweight geodesic domes to advance bases by helicopter. This could be done without taking the domes apart, for the helicopters were able to pick them off the ground at one place and put them down at another, ready for immediate use. Time for erection: zero. These Marine Corps domes were stronger, larger and otherwise more satisfactory than tents. In the scheme of military logistics, they could displace both the tents of advance bases and also the more permanent structures of intermediate supply bases. They could be first to arrive, for speed, and after that could remain, for permanence.
48 Impetus derived also from the suitability of the geodesic dome for transport and erection at distant sites in far northern territories to house electronic systems for hemisphere defense. For this purpose, structures of geodesic form were made from translucent plastic. Their components were molded into plastic pans. The flanged edges of the pans were color-coded for bolting together in the particular way that would bring physical realization of the great circle integrity which is the essence of the system now known simply as ‘‘geodesics.’’ The first hemisphere defense system, housed within a far-flung chain of these plastic geodesic domes, called Radomes, is the one commonly referred to as the DEW (distant early warning) LINE. It reaches from Cape Lisbume, Alaska, to Baffin Island, 3,000 miles of electronic ears. A second defense system, similarly housed in geodesic domes, is furnished by BMEWS (ballistic missiles warning system).
49 Requests for licenses under Fuller’s geodesic patents came from manufacturers wishing to supply the government with Radomes or Marine Corps shelters. Such was the starting spur to a broadening use of geodesics. But this was preceded by the work of a small group of architects and engineers who had been inspired by Fuller’s teaching. In university classrooms at North Carolina State, Tulane and Harvard (and elsewhere), students had been acquiring fundamentals of the new geometry and learning its application by designing and building on campuses geodesic domes in as wide a diversity of forms as its geometry and their own imaginations might contrive.
50 The quality of Fuller’s teaching was such that a number of his students were inspired to make of geodesics a life work. This group of students soon became, in effect, a practicing school of architects, a small but earnest coterie who were able to speak the new language of geodesics and synergy, and who had the capability of translating this language into architectural reality. In time, and with their teacher’s own encouragement and financial backing, these graduate student groups founded design centers for geodesic construction which emerged corporately as Geodesics, Inc., and Synergetics, Inc., of Raleigh, North Carolina, and Geometries, Inc., of Cambridge, Massachusetts.
51 The Raleigh group, led by James M. Fitzgibbon, was encouraged to concentrate its primary effort in the commercial applications of geodesic architecture, and was responsible for designing and supervising the erection of the largest freespan structures ever built, two railroad roundhouses for repair and maintenance of rolling stock of the Union Tank Car Company, the first erected at Baton Rouge, Louisiana, the second at Wood River, Illinois. Domes built of steel plates and tensile struts, these were buildings so vast as to be capable of enclosing the largest football stadium—playing field, spectator stands and all. But so light and thin in relation to their vast proportions that their shells are thinner than that of an eggshell in relation to the egg.
52 The Cambridge group, led by William Wainright, concentrated much of its early work on designing for the nation’s defense establishment, and was responsible for calculating the spherical geometry of the plastic domes for electronic defense networks. This, as we have seen, was instrumental in spreading interest in geodesics across a wide spectrum of United States industry, which in turn created a demand for patent licenses under the rights held by Fuller. Patent Divisions of the Army, Navy and Bureau of Aeronautics, and patent law firms representing some of the largest corporations, subjected Fuller’s patents to the most searching investigation before permitting the government to approve or the corporate clients to pay modest royalties for the right to use die patented inventions. It is to be doubted whether any other patent situation has ever been subjected to closer scrutiny by the government which granted the patents, or by a more impressive roster of patent counsel asked to advise their corporate clients, than in the case of those ordered to investigate and advise whether Fuller’s patent rights should be respected. A leading patent lawyer, long regarded as dean of the Chicago patent bar, confided to the author that in his practice which extended over half a century, he never had had the privilege of reading a more original and impressive document than the fundamental geodesics patent of Buckminster Fuller. ‘‘I am advising my client to take a license,’’ he concluded.
53 A concomitant of the demand for licenses was a need for the engineering skills of the men and organizations who had become practicing experts in the new field. And so, if the defense establishment of the nation was ready for geodesics, it can be recorded that geodesics was ready for the nation. The specifications, once written, could be met almost head on with designs ready for the building. Before long, streams of plastic Radome components were winging their way to Arctic outposts, ready to stand against icy gales and hostile intentions alike. Other streams were flowing to the Marine Corps.
54 Alertness to the potential boons promised by the new architecture was not confined to the government and defense, for the year 1956 also saw activity in the world of commercial building. Under license from Fuller, Kaiser Aluminum envisioned and designed a geodesic structure incorporating added features created by its own engineers. This was an aluminum dome which could be tailored to a variety of purposes, and which the Kaiser organization produced and erected for banks, factories, theaters, shopping centers, sports arenas and other uses.
55 IN contemplating the modus operandi of the mind of the inventor, it will be useful to consider what was the preoccupation of that mind during the year 1956 that we have just watched go by with its procession of flying Marine Corps shelters, defense lines of Radomes, and theaters, banks, and arenas. To what extent might Fuller’s inventive urge be distracted by the burgeoning success of ‘‘the dome’’? A less dynamic mind might be likely to find its course magnetized in the direction that fame was taking, but not Fuller’s. For him, 1956 was only the beginning of an inventive stream of wider implications in synergetic building construction spreading beyond the dome. This stream was to include tensile integrity trusses useful for rectangular buildings as well as domes, ‘‘suspension’’ buildings, and structures stressed so purely in tension that the minimal compression elements would not even touch one another for transmission of loads. Even undersea islands, anchored ‘‘tetrahedrally’’ in accordance with the form discovered by energetic/synergetic geometry as the first identifiable system in the universe. The deep current of Fuller’s thought was too strong to feel influence from temporal advantage. As the licensing royalties flowed in, they were as quickly distributed among those who had shown their willingness to plight their faith with Fuller’s. The money went back into the business that had made geodesics ready for the needs of a nation, that of Fuller’s former students, then executives in the architectural and manufacturing companies that continued to be the spearheads for testing and introducing the inventor’s most advanced concepts in the geodesics field.
56 The broadening stream of invention was signalled by the filing in 1956 of Fuller’s application to patent ‘‘synergetic’’ building construction. The patent was granted in 1961.5 How could the benefits of geodesic dome construction be extended to more conventional building forms based on the rectangular prism rather than on the sphere? Was there a synergy of forces that could go beyond that discovered within the sphere's great circles? We have learned about the tetrahedron, the geometric figure having four equal equilateral faces. And Fuller has explained that this is a system having applications so wide and varied as to be thought universal. Now Fuller examines the octahedron, which displays eight equal equilateral faces. According to the new invention, both octas and tetras are combined to make a truss system in which these two kinds of geometric figures are congruent. Fuller found that ‘‘if any flat roof, wall or floor framework is built up of struts (or sheets) of equal length in such a fashion that such elements are comprised within a common octahedron-tetrahedron system, the strength of the framework is far greater than would be predictable using any conventional formulae based on resolution of forces and known values of strength of materials.’’6 So, Fuller continues, ‘‘In fact, my practical tests have shown that the actual strength of these flat one system octahedron-tetrahedron structures so far exceeds calculated values as to suggest a hypothesis that such structures are ‘synergetic’ in the sense that we have a stress behavior in the system which is unpredicted by its parts.’’ Unpredicted, synergetic, a structure now known as the ‘‘Octet truss’’ or simply, ‘‘Octetruss,’’ oct for octahedron, tet for tetrahedron. It is a system made up of four unique sets of parallel, symmetrically oriented, omni-triangulated planes. For simplicity, we can say, four unique planes. There is a singleness in the system which allows it to carry through the roof, floor and wall sections of a building in a manner akin to a crystalline growth. A servicing dock for a B-26 bomber constructed according to this invention would have a weight of only 0.115 pounds per cubic foot of space enclosed, and when the parts of the dock are disassembled, they will pack for shipment into l/350th of its ultimate cubic enclosure.
59 It could now be seen that Fuller’s plan of turning the energies of the universe to greatest human advantage extended beyond limitation in form or shape of a building. As the cube did not restrict his thinking, neither did the sphere. The tetrahedron had proved to be a least common denominator of prismatic and spherical structures. As with his mathematics which came before, the ultimate significance of Fuller’s inventions lay in universality of application. It was not the visible shape that counted, so much as it was the dynamics of a far more sophisticated concept. Not just a dome or a truss as such, but a complex whose structural stress behavior as a whole was truer to the underlying dynamics of all creation. A structure which, regardless of the materials that went into it, was compounded much of energy and synergy, little of material. In a meaningful sense, it could be called a structure made of energetic/synergetic geometry. Here we are thinking generically both of Fuller’s geodesic dome and his octetruss, which, though not visibly alike to any eye but a mathematician’s, are bonded by pattern of stress behavior and a common philosophy of conserving material resources through tapping energy sources. Statically un- alike. Dynamically alike. In life itself, energy of motion is the universal equation; the material is of lesser significance. For the material can be transformed, while the energy lives on. Fuller’s thought patterns never were disassociated from the universal equation.
60 FOLLOWING his discovery of a structural equation which brings buildings of visual dissimilarity into an energetic/synergetic likeness, Fuller came upon another discovery of a most unexpected nature. He had been experimenting with constructing domes made of plywood. It occurred to him that it might not be necessary to cut the sheets of plywood into triangular shape before fastening them together into a geodesic dome. Why not just use the flat rectangular sheets in their common four-foot by eight-foot form, simply letting them overlap as they might while following a pattern in which the centerlines of the sheets would be aligned with the great circle-based three-way gridding of geodesics? When he tried this, and fastened die sheets together where their corners overlapped, an amazing transformation took place. A pair of triangles, together making a diamond, formed themselves within the rectangular outline of each plywood sheet! The triangles had not been there before. Fuller had not made them. They simply emerged out of nowhere—or from Nature as is usually the case where that kind of a ‘‘nowhere’’ is concerned. The dome had in some natural way made its own geodesic struts—a ‘‘self-strutted’’ dome, as it was named in the patent.7 The flat sheets had, by pure self-inductive action, become geodesic. They became, Fuller announced, ‘‘both roof and beam, both wall and column, and in each case the braces as well.’’ Further explaining his discovery in the patent disclosure, Fuller said:
6263They (the flat sheets) become the weatherbreak and its supporting frame or truss all in one. The inherent three-way grid of cylindrical struts causes the structure as a whole to act almost as a membrane in absorbing and distributing loads, and results in a more uniform stressing of all of the sheets. The entire structure is skin stressed, taut and alive. Dead weight is virtually non-existent. Technically, we say that the structure possesses high tensile integrity in a discontinuous compression system.
64 Again perception of the ‘‘aliveness’’ of synergetic building. Again Fuller’s strong urge to discover optimum tensile integrity. In this instance, the tensile integrity had literally sprung into self-manifestation. The inventor had aimed the sheets in the direction of a geodesic pattern, and—lo and behold—the final pattern had emerged by itself. It was almost as though he had only to suggest to the plywood sheets that they were laid up icosahedrally, and that they had answered, ‘‘So we must fall into a full geodesic pattern.’’ Or simply, ‘‘We want to be geodesic.’’ (Like the dome that Fuller said ‘‘wants’’ to stand up, and the conventional building that doesn’t.) A comprehensive truth had asserted itself. It had spoken spontaneously, for not even in his most excited imagination had Fuller foreseen that triangular strutting was going to appear by inherent geodesic force reaction.
65 Yet once discovered, such inherent force reaction is demonstrable in an extremely simple way. For the demonstration, it is necessary only to grasp an ordinary three-inch by five-inch file card by the tips of the fingers, two fingers of one hand touching the comers at one end of the card, and two fingers of the other hand touching the comers at the other end. Then the four comers of the card are urged downward and slightly toward one another. The triangles will at once display themselves to view in the form of rounded fold lines. This rather oversimplified demonstration does not reach the sophistication of Fuller’s discovery as related to geodesic patterning, but it will serve to explain what is meant by the term ‘‘self-strutted.’’ Self-triangling.
66 The overall pattern of triangles that is distinctive of geodesics could be made from rectangles. And from what else? If a structure somehow had been programmed to produce a pattern of triangles from rectangular sheets, what might be the possibility of having the same programming create its progeny of triangles from sheets of still other forms? From his discovery up to that point, Fuller knew that the rectangular ‘‘file cards’’ would work, but if not triangular to start with, need they be rectangular? What was the broadest range of possibilities? This kind of extrapolation was instinctive with Fuller, so that he quickly realized that the genus of his invention definitely was not the rectangle. The rectangle was a special case. No, the genus would necessarily be a flat sheet of no particular shape. Formless, an amoeba. Spontaneously his pencil traced a shapeless blob on the paper napkin spread out on the table to explain to his patent lawyer the esoterics of self-strutted buildings. ‘‘The starting sheets could be leaf-shaped, any shape at all,’’ said Fuller. His lawyer pursued the wrong end of the sentence, momentarily entranced by the thought of a leaf-shape, and losing the emphasis on ‘‘any shape.’’ ‘‘What interesting effects would be possible by using special shapes such as leaves!’’ exclaimed the lawyer. Patient in reproof, Bucky, the teacher, replied in a voice of almost caressing softness, ‘‘We are not interested in ‘effects,’ now are we?’’ Well there it was, a clear lesson in the motivation of a mind such as Fuller’s. Naturally that mind could not be concerned with effects as such. The effects could not be sought.8 Yet we can imagine that the architecture produced through comprehensive thought should perforce be pleasing for the eye to see. This for the very reason that it expresses Fuller’s thesis of turning the energies of the universe to human advantage. Natural, therefore inherently pleasing. At any rate, the teaching now is crystal clear. The overlapping sheets could be of any shape imaginable, or of assorted shapes, and the part of nature that is geodesics will make them bend into triangles whose edges create a geodesic form that is strong, stable, and synergetic.
68 Later in the day of the lesson that geodesic design should never concern itself with ‘‘effects,’’ we were privileged to accompany Fuller on a visit to a prototype self-strutted dome. It was one which was designed to serve as a farmhouse and was located in the vicinity of an Iowa village, Van Meter, perhaps an hour’s drive west of Des Moines. The visit came on a cold day that eased the mercury twelve degrees below zero, and the domical shell of the farmhouse-to-be rose stark and frozen from a powder blanket of snow. But not stark really, for the sheer symmetry of its geodesic form made it at once a thing of beauty and as much at home on the bleak landscape as an igloo on an ice floe—to which it indeed bore resemblance. The door opening was just that, for no door had been hung in it, and you recoiled an instant from stepping into inside cold. But once in, a surprising breath of warm air brought a welcome caress to frosted faces. ‘‘How in the world can it be so warm in here?’’ you thought, glancing back at the open doorway and hearing the wind. At the far side, opposite, a tiny New Perfection oil stove was unconvincing although there was a bit of a flame within.
69 ‘‘So,’’ said Bucky, answering the unspoken question, ‘‘You see why the Eskimo builds his house in the round.’’ Then to make the demonstration complete, ‘‘Stand here inside the doorway.’’ We did. ‘‘Now extend your hand slowly toward the opening—first take off your glove—and tell me when it feels cold.’’ Six inches inside the opening, warm. In the plane of the missing door, freezing cold. ‘‘The explanation?’’ asked the inventor, ‘‘Well, what happens is, that inside of a dome the warm air rises to the apex and then, cooling, slides down along the sloping walls until it reaches the floor. This descending air, still warm though cooling, forms a warm curtain which maintains a surprising integrity as it passes down across the door opening, influenced more by the natural convection currents inside than by the wintry blasts outside.’’ This added virtue of the dome has earned appreciation by the personnel of bases in polar regions where the geodesic dome has been used to advantage. It should be stated, parenthetically, that such use stemmed from recognition of lightness and ease of transport by air. That the dome could be heated so efficiently was simply an extra dividend.
70 Turning from the still cold-looking doorway which our minds now saw warmly curtained, eyes were lifted to the apex of the dome with much the same magnetism that one experiences as his spirit soars upward to the groined ceiling of a Gothic cathedral. A geodesic dome always surprises with a sense of its immensity. This Iowa farmhouse was a 42-footer, no more (42 feet in diameter at its hemispheric base), but it was overpowering in its seeming vastness. As in the cathedral, spirits soared and we stood in a world apart from the Iowa winter.
71 BY the spring of 1958, the number of Fuller’s licensees had risen to sixty-one. A company called Plydomes, Inc., had been formed to produce the self-strutted dome. In 1959, Fuller filed for a patent on an invention entitled, ‘‘Tensile-Integrity Structures.’’ Study of the previous inventions in geodesic structures shows that ‘‘tensile integrity’’ is a term that had been used from the beginning to describe a principal characteristic of such structures. It meant continuity in the pattern of tension forces throughout a structure. Tension was relied on more, compression less. More pull, less push, and therefore greater use of what is best in structural materials—their strength to resist pull. What was most significant about the 1959 invention was not that it was named for tensile integrity, but that it was a comprehensive, daring exploration of the outer limits of tensile force availability in architecture. How fully could man avail himself of the rich store of tensile strength in his new materials? How pure a tension structure could be contrived? How far could we go in the direction of eliminating compression altogether? The tensile integrity invention provides the answers. Also it has the capability of revealing visual manifestations of its use of tension, or more accurately some aspects of such use. This capability is demonstrated when the tensile network of a structure is physically constituted in the form of wires, for the wires are easily understood to be stressed purely in tension. So in this sense we ‘‘see’’ the tension.
72 A first look at a dome or sphere made according to the invention can be deceptive, for it may
not be noticed that the minor elements of the structure, the compression struts, are not actually
in contact with one another (discontinuous compression). One does see much of the now familiar
geodesic pattern, the triangles, hexagons and pentagons of the icosa progenitor, and the
uniformity of its non-polarized de
sign. A closer look, and a first new aspect appears in the strange, ‘‘spikey’’ form that provides a
clue to ‘‘discontinuous compression.’’ The spikes are the ends of the compression struts all of
which are out of touch with one another. Now
73 the significance of the network of wires is perceived, and one discovers that those struts seem just to float in the lacey net of wires. This is a baffling moment, for the mind has difficulty in comprehending why the net of wires does not collapse like a fishnet with its catch of fish, the floating struts. What keeps it all standing, as though it had an impervious skin and gas inside to make it a balloon? The fact that it did stand brought dawning realization that Fuller had accomplished a farther-reaching breakthrough in the optimum use of tensile force.
74 ‘‘The essence of my invention,’’ said Fuller in his tensile integrity patent,9 ‘‘consists in the discovery of how to progressively reduce the aspect of compression in a structure so that, to a greater extent than has been found possible before, the structure will have the aspect of continuous tension throughout and the compression will be subjugated so that the compression elements become small islands in a sea of tension. This is to bring the slenderness, lightness and strength of the suspension bridge cable into the realm previously dominated by the compression column concept of building.’’ ‘‘Small islands in a sea of tension’’—what before had been the dead weight of columns and beams brought down at last to the irreducible minimum in the form of these little islands floating in a gossamer web of tensioned wire.
76 Difficult as it may be to see in the mind that which the eye sees only as a building ‘‘standing’’ mysteriously on an apparently unsupported flexible maze of wires, this is only part of the problem of bringing the total complex within reach of ordinary comprehension. For the rest, we must attend to Fuller’s explanation of why it is that what the eye sees as a single island is functionally not one island but two. Yes, this means that there are twice as many functioning compression islands than are to be counted when one adds up the total number of struts present in the structure.
77 ‘‘My tensegrity structure,’’ said Fuller, ‘‘comprises struts arranged in groups of three, overlapped to make a tripod as in an Indian tepee.’’ Unlike the tepee, the struts do not touch one another where they overlap. These three struts are the three axes of our old friend, the octahedron. When wires join together the six ends of the three struts, an octahedron is formed. The octahedron comprises the ‘‘primary system’’ as one component of the tensile integrity complex. This primary system is visible only to the mind’s eye. First, because when one primary system is joined to a second, an octa axis (strut) of one is physically connected to an octa axis (strut) of the other. As the complex is expanded to include additional primary systems, all the axes are so interconnected. Second, because in the total tensegrity complex the wires which otherwise would have made visible six of the twelve edges of each octahedron are physically omitted.
78 Here we have two realities which the mind sees, but the eye cannot; and one unreality which the eye sees, but the mind should not. So strange a state of affairs deserves closer study:
7980The physical joining of struts of adjacent primary systems (the tepees) is described by Fuller as creating ‘‘ ‘apparent’ compressional continuity.’’ Actually the struts so joined apparently into one are functionally two, because the tension wires of one tepee pull in one direction away from the center of the strut that is visually one, and those of the other tepee pull in an opposed direction away from the center of the same strut. Thus one end of that strut acts functionally as one compression column, while its other end acts as another compression column. Two separately acting columns in one ‘‘apparent’’ column. The ‘‘apparent’’ column is therefore said to be in ‘‘discontinuous compression.’’ A second aspect of discontinuous compression lies in the physical separation of one pair of physically joined struts from another pair of physically joined struts. This the eye can see. But the first it cannot.
81 And as to the visual obscurity of the primary octa system by reason of the possibility of omitting tension wires which if present would lie along six of the twelve edges of each octahedron, the inventor tells us:
8283The omission of such wires tends to obscure the visual appearance of the eight triangular faces of the octahedron, but does not destroy the octahedral aspect of the primary system that is necessarily fixed and predetermined by the presence in the system of the aforesaid six vertexes which characterize the octahedron.
84 It all adds up this way:
85 Realities which the mind sees, but the eye cannot—
- a.
- Two functioning struts in what physically looks like one.
- b.
- Functioning octa systems in a complex which does not physically reveal complete octas.
86 An unreality which the eyes sees, but the mind should not—
- c.
- A strut that is physically one, but functionally is two.
87 It will be recognized that (c) is the converse of (a), but completeness of analysis demands statement of both. The reason is that in (c) the eye actually sees an unreality, whereas in (a) there was only the failure to see reality.
88 So what the mind sees in the tensile integrity structure of this patent, while invisible, contains more of the true reality than what the eye sees. Conversely, in one particular what the eye sees in that same structure is in fact unreality. The ‘‘real’’ is understood to be the unreal, and the invisible to be the true reality.
89 Where such is the quality of invention that its physical embodiment makes invisible its functional capabilities, of what avail is the pictorial representation of the physical embodiment? If pictures can be so misleading as to make us see something that is not real while failing to make visible what it is that makes the invention work, we have the case where words are better than pictures for explaining that invention. Or, as suggested in the beginning, perhaps even better than pictures explained.
90 It will be of interest here to observe the difficulty experienced by the patent examiner in Washington when faced with the challenging assignment of analyzing and acting upon Fullers application for his tensile integrity patent. The examiner, studying the patent drawings, apparently found his mental vision obscured by his physical vision. So much so that at first he misunderstood the meaning of the accompanying explanation of the invention, and afterward disbelieved the explanation, evidently having had his mind too far clouded by what he had seen in the drawings. Here then was an example of the problem noticed in the beginning, of how best to explain the discoveries of Fuller when we understand that they probe so deeply into the unseen dynamics of force and motion. In the case of the patent examiner whose only difficulty was that he had allowed his visual perceptions to cloud those of his mind, the simple solution was to suggest that he lay aside the patent drawings and listen to a fresh explanation of the unseeable aspects of the invention, starting all the way back with that primary tensegrity, the octahedron. Soon the examiner found his mind soaring into the realities of the largely invisible but very real world of tensile integrity structuring, and the patent was granted.
91 On one occasion Fuller was invited to be a special guest speaker at a meeting of The Patent Office Society, an organization of the active examiners of the United States Patent Office where the meeting was held. The officers of the Society stated that Professor Fuller was the first inventor who had ever been asked to address the examiners at such a convocation insofar as their records showed, and was certainly the first to be so honored within their memory. The meeting was in the afternoon, and the examining staff was given time off so that if they chose they might avail themselves of the opportunity to hear the illustrious inventor. There was a record attendance of over eight hundred examiners. Obviously entranced by Fuller’s zeal as he led their trained minds deep into his own philosophical approach to invention and patents, the seats of the government auditorium across the street from the Patent Office were still filled two and a half hours later, although it was then well past working hours. As Fuller concluded his address, a score of examiners pressed eagerly around him. Among them were two who were responsible for acting on certain Fuller applications then pending. Each of these in turn identified the invention described in the case he was handling, asked a question or two about it, and concluded with assurances that an early allowance of Fuller’s claims could be expected. Fuller had unwittingly become his own skillful advocate before the Patent Office. He possessed a firm grasp of the requirements of the patent law for patentability. Aware that an invention to be entitled to the patent grant must be unobvious, he had as a rule been alert to inform his patent counsel whenever an invention of his brought results that he had not expected. Such a result he would always refer to as a ‘‘surprise.’’
92 The patent examiners generally were impressed by Fuller’s surprises. But these same examiners, and those of other patent offices round the world, used to have quite a problem in becoming accustomed to Fuller’s new vocabulary of geodesics. Although the vocabulary was one that had become the everyday working language of practicing experts, and was familiar to students in Fuller’s university classes on virtually every major campus in the United States and those of many nations and on all the continents, it was yet too early to expect to find the new words in the recognized dictionary sources. So, many examiners were unready to tolerate the language even though reminded that it is settled law that ‘‘an inventor is his own lexicographer.’’ In the end, most had to acknowledge that new art must create new language. Today, that new language has become essential semantics not only to the mathematician and architect, but also the accepted language of the patents in the field.
93 SOON after his invention of tensile integrity structuring, Fuller became intrigued with the possibility that his lightweight geodesic structures might be made lighter still. Monsanto Chemical Company had been attracted by the self-strutted dome. As it could be made of flat plywood sheets, the company foresaw a new use for its polystyrene laminates. These comprised a core of expanded polystyrene faced with sheets of paperboard or plastic. With such styrofoam laminates it should be feasible to construct feather-light geodesic domes. They would be useful as shelters for many purposes, for example as low-cost ‘‘on site*’’ warehouses in the building construction field.
94 Probing for the optimum in simplicity, Fuller conceived in the spring of 1960, a geodesic dome that was well suited to the Monsanto venture. It could be built with the use of just two kinds of panel components, each of diamond shape, and appeared to represent the ultimate in simplicity of design, parts stocking and erection. Also, it possessed the advantage of being ‘‘truncatable,’’ meaning that it was adapted to making a shelter of selectively variable height according to particular needs. At one height it would be in the form of one half of a sphere. For less height, it would have the form of three-eights of a sphere, for greater, five-eighths. The feature was that whichever the line of truncation that might be selected, the ground line of the building will be straight. This was accomplished through a special design of the spherical geometry of the dome which brings edges of the diamond-shaped panels into alignment at each of the three lines of truncation. Hence there is no need to provide special foundation line ‘‘filler’’ panels as would otherwise be the case. The same geometry created also the further simplicity of componentation which narrowed the number of panel types to two, as stated.
95 The secret of the geometry lies in the relationships between the lengths of the sides of the diamonds and between their long and short axes. These relationships are expressed as chord factors. Six diamond panels are so grouped that the vertexes of the acute angles at one end of the long axis of each meet at a common point, three of the six sections of the group having the following chord factors:
9697Sides adjacent said acute angles = 0.42 Remaining sides = 0.33
98 Short axis of the diamond = 0.38
99 and the other three of the six sections being alternated with the first three sections and having the following chord factors:
100101Sides adjacent the acute angles = 0.42 Short axis of diamond = 0.44
102 Long axis of diamond—0.71
103 These are the particular relationships which yield both truncatability and two-component simplicity. No theory need be suggested to explain why this is so, for here the mathematics did not sire the invention. Instead, the invention discovered the mathematical formula, empirically. This is remarkable because it shows again the pervasive influence of Fuller’s mathematical mind. Even if mathematics was not progenitor of the invention, this circumstance did not preclude him from finding a way to define it by arithmetic formula.
104 The patent for this invention10 is of special interest for another reason, as it affords a penetrating example of Fuller’s sensitive awareness of reality in what cannot be seen. So sensitive is his awareness in this instance that it enables him to discover a fact that is in direct opposition to that which our eyes, in error, would make us believe to be true. This is disclosed in the inventor’s analysis of the phenomenon of truncatability. He observes that two of the lines of truncation look like what are known as ‘‘lesser’’ circles (as opposed to great circles) such as the lesser circles comprised in the parallels of latitude of a standard globe in which the equator and the meridians are the only great circles. Yet in the dynamics of geodesics these two lines of truncation are not the lesser circles they would appear to be. Functionally, they are chordal modules (parts) of great circles. Fuller demonstrates this through a brilliant probe into the geometry of the spherical icosahedron. In characteristic manner, he instinctively returns to the genesis of geodesics and infallibly drives through to the true dynamics of its truncatable form:
106107Particular attention is directed to the fact that the chordal modules of the lines of truncation, when viewed in one aspect, appear to be chordal modules of lesser circles. However, by construction upon the spherical icosahedron wherein all of the vertexes, and therefore both axes, of the diamond panels lie in great circle planes, these chordal modules in reality lie in planes passing through the center of the sphere whose intersections with the sphere describe great circle arcs. The phenomenon of alignment of panel edges for truncation may be described as the ancillary appearance of small circles, which may be likened to the parallels of latitude of a standard globe of the earth, at the three- eights and five-eighths lines of truncation occurring, however, as incidents of true great circle, i.e. geodesic, construction.
108 So the unapparent great circle modules are dynamically real, and the ‘‘apparent’’ lesser circles are unreal in geodesics (albeit real in the sense of ancillary availability for base line truncation). Or at least the ‘‘apparent’’ is real only in the sense of visual statics. Fuller’s mind, intuitively or through practice as the case may be, unerringly searches out the total of reality in terms of the dynamics of universe. His mind’s eye does not let him be fooled by his optic nerves.
109 AN added catalyst to the widening of Buckminster Fuller’s vision during the 1950s and 1960s was provided by the stepped-up tempo of his travels. Everywhere in swift succession there were classes to be taught and speaking engagements to be met. The demands on his time were multiplied to the extreme so that sometimes, after flying half round the world, he would be addressing one meeting in the afternoon, another in the evening and a third the following day. When the third happened to be in another city, the schedule could become a little rigorous even for Fuller! If anyone could ‘‘fill the unforgiving minute with sixty seconds worth of distance run,’’ Fuller was Kipling’s man.
110 Could else be needed to give his mind the comprehensive touch, it was furnished by a galloping world perspective as daily he touched the minds of others all round Earth’s compass. These others included persons of many callings, for Fuller’s teaching was sought not alone by scientific and architectural groups, but also by businessmen, economists, lawyers, doctors, educators and statesmen alike. From his own United States to distant India, from Japan to South Africa, Fuller labored on, and grew in the esteem and affection of all whose minds he touched. His were the diverse roles of college professor and personal confidant of leaders of state. Meanwhile he called unceasingly on strong reserves of energy as he met ever tightening schedules of work and travel, forever eager to feed the imaginations of all who were striving for new understanding and purpose.
111 As Fuller taught, he also listened. As he listened, he translated. As he translated, the scope of his teaching grew. The effect was regenerative as the teacher’s mind responded to the expanding thought pattern of the student. Full pt describes this sort of response as ‘‘positive feed-back,’’ the process by which one idea fed into his mind from any observed or translated experience of man generates a family of related ideas from which a broader generalization of the beginning idea emerges. All of us possess to a greater or less extent this capability of developing the general from the specific, and of being aided in the process by interchange of ideas with others. With Fuller, the regenerative process plays a peculiarly dominant role. How the process works in his comprehensive thought climate is disclosed by a case history. The history is one which will reveal also something of the incredible tempo of Fuller’s inventing.
112 As 1961 became the new year, Fuller conceived his invention of the suspension building. He himself recounts the facts leading up to the invention:11
113114On or about December 20, 1960, I received by cable an invitation from Mr. Shoriki, Chairman, Nippon Television Network Corporation, to come to Japan for the purposes of (1) studying the possibility of constructing an indoor baseball stadium, and (2) making popular lectures on the United States modem architecture in Tokyo, Osaka, Sapporo and other several cities in Japan. This was confirmed by a formal letter invitation received immediately before Christmas. A similar invitation was received by my associate, Shoji Sadao of New York City, on December 26,1960.
115My first thoughts related to the idea for my invention came to me during the first contemplation of a possible trip to Japan, and took form in my mind only after receiving the invitation before Christmas of 1960.
116Then, during the Christmas holidays, namely between Christmas and New Year’s, I conceived my 11 invention substantially as disclosed in the forms illustrated in Figs. 4, 5 and 7 of my patent application.…These concepts even then were only worked out in my mind, but I decided that the subject matter was of such interest and promise that I would want to make a disclosure thereof when I reached Tokyo. So I immediately got in touch with my associate, …Shoji Sadao, by long distance telephone and described my mental concept to him with the request that he prepare sketches with all possible speed for the use of my attorney in preparing a patent application. This disclosure to Mr. Sadao was accomplished within a matter of possibly one, two or three days after conception and between Christmas Day 1960 and New Year’s Day 1961.
118 Fuller had transmitted an understanding of his invention from Los Angeles to New York by a telephone call made within at most ‘‘three days’’ after conception. Then, Fuller continues,
119120During the ensuing period between New Year’s Day 1961 and January 19, 1961, the concept continued to fulminate and on or about January 19, 1961,1 conceived the embodiment of my invention as represented in Figs. 18 and 19 of my application for patent and disclosed it to my patent attorney by telephone call made from Texarkana, Texas, to New York City. Other forms as depicted in Figs. 1, 2, 3 and 8--17 inclusive, were conceived in the period between January 9, 1961 and January 19, 1961.
121 On January 9, 1961, Fuller’s associate, Shoji Sadao, furnished Fuller’s patent attorney a first disclosure of the invention including preliminary sketches showing a number of its embodiments. At the same time the attorney was told that Fuller was going to leave for Tokyo where he expected to arrive early in February and to be called upon to make at once a full disclosure there, most probably of a public nature. This anticipated chain of events created a pressing legal problem, because, under Japanese law, a public disclosure of invention before the filing of a patent application would preclude valid patenting in Japan. But if within the limited time remaining before Fuller’s scheduled arrival in Tokyo an application could be prepared, signed and placed on file in the United States, the problem would be solved. For by treaty12 the United States filing date could be claimed as the effective filing date of an application filed in Japan within a year afterward. The race to place a complete specification and formal patent drawing in Fuller’s hands for signing before his plane would be taking off for Japan was hampered by the circumstance that Fuller was then in California, his attorney in New York City. On January 9, the same day that the disclosure was received by the attorney, sketches for patent drawings were made. Also on that same day these sketches were sent by wirephoto to Fuller, then in flight between Los Angeles and San Francisco.
123 Among the wire photos there were included sketches of a number of additional embodiments of the invention born of analysis of the inventory disclosure by the attorney and his patent draftsman. The draftsman13 was an accomplished artist whose mind was acutely sensitive in its responsiveness to the underlying currents of Fuller’s thoughts and philosophy. Quick to sense the generic thrust of the invention, he created in dry point several alternate forms that the disclosure brought to his mind. These were the additional embodiments which have been referred to as being included in the wire photos transmitted to Fuller for approval. Upon the inventor’s examination of the photos, there occurred the feed-back of his original idea, expanded to test scope of invention insofar as could be imagined by draftsman and attorney. The result, as Fuller said, was that ‘‘Other forms [of the invention] were conceived in the period between January 9, 1961 and January 19, 1961.’’ These other forms went distances beyond anything discoverable by visual examination of the wire photos. They were the direct product of feed-back of intelligence and ensuing gestation by a mind characteristically free from formal knowledge limitations. Reason suggests that it is this freedom which affords to Fuller’s mind its increased potential for regenerative action.
125 On January 19, Fuller’s description of the additional forms of his invention reached New York. Within the ensuing twenty-four hours, drawings- were made of these forms and the formal patent papers made ready for signing. These were carried by hand to a rendezvous at the mid-continent airport of St. Louis where Fuller was intercepted on a flight from Illinois to the west coast on the first leg of his trip to Tokyo.
126 As the days and hours were harvested and gleaned of every last minute in the hurry to put the necessary documents into the Washington patent office before the moment of Fuller’s arrival in Tokyo, a tiny gap appeared. There had not been enough unforgiving minutes to get all the ink on the patent drawings, so they had to be left partly in pencil. Formal requirements of the patent rules had not been met fully. In the end, the Patent Office waived such requirements as was permitted where sufficiently unusual circumstances warranted. But in sharp contrast of tempo, it took seven months for the Office to grant the waiver. Seven months to decide that Fuller had acted as fast as he should! In a decision by the First Assistant Commissioner of Patents taken May 18, 1961, it was suggested, ‘‘…no showing has been made in the instant case why the applicant did not authorize the preparation of the application earlier in view of his impending trip to Japan.’’ The Commissioner had managed to overlook the statement made in Fuller’s petition that he had ordered preparation of his application within at most three days after conception. Fuller answered simply, ‘‘The reason why I did not authorize the preparation of my application at an earlier date than I did, was that I had not made the invention at any earlier date.’’ His petition was granted, and the filing date of January 24, 1961 was awarded. The race to Washington had been won. It was February when Fuller arrived in Tokyo and disclosed his invention to the excited Japanese. His right to patent protection in Japan14 had been preserved. And so, against this backdrop of frenzied patent activity, the suspension building was unveiled in a forward-looking Japan. This building was another part of Fuller’s tensile integrity frontier. It can be imagined as consisting essentially of an ascending series of rings in the form of curtain walls. Each ring of the series in smaller than the one below it, creating a visual similarity to a pyramid, particularly when the rings are square. Unlike the pyramids of Egyptian antiquity, the upper layers are not piled up on the lower ones. Instead, each succeeding ring is suspended from the one below it. The general principle is to run supporting wires or cables from the upper part of a lower ring to the lower part of an upper ring. Following the same system, it is possible to create many different forms of building, including tire domical form of the geodesic dome. Fuller said, ‘‘I have discovered how to make building structures and components possessing in substantial measure the advantages of catenary suspension heretofore confined principally to the suspension bridge. The catenary cables of the suspension bridge sag downwardly to the mid-point of the bridge, and would seem to possess no utility in any structure which arches upwardly. So it has been a surprise to me to find that there is a way by which a catenary suspension system can be converted into an arched structure of domical or polygonal form. By breaking up the suspension cables into increments suspending an ascending series of polygonal or circular frames stepped upwardly one within another, altitude is gained, replacing the catenary sag of the bridge cables with a rising, arched, suspension system.’’15 So a sort of upside down suspension bridge system becomes a building. Small wonder that the impressionable Japanese were excited. FULLER’s translation of building to geometry, or geometry to building, continued. In December of 1961 he filed application to patent16 what he called ‘‘hex-pent’’ construction, a name easily recognized to be derived from the hexagon and pentagon of the geometer, figures of six sides and five sides. Again there is geodesic construction based on our old friend the spherical icosahedron, comprised of twenty equilateral spherical triangles. Fuller makes certain that our mathematical profundity will be sufficiently deep, as he explains with great care that instead of twenty triangles per sphere there can just as well be the twelve spherical pentagons of the dodecahedron. (The dodeca is the inversion of the icosa.17) Not only that, but as a further alternative there can be the thirty spherical diamonds of the tricontahedron, for in the art of geodesics the same division of the sphere results regardless of whether one considers that the breakdown has been based upon the icosahedron, the dodecahedron or the tricontahedron.
131 Starting, then, with any of these three spherical polygons, a variety of structural forms emerges. Looking unalike one another, the least common denominator of their interrelated energy geometry makes them functionally and dynamically alike. The hexagon furnishes the key to the invention which consists in a framework including six-sided panels, three sides straight, three curved. The three curved sides of adjacent panels form circular openings. Here appears the tensile integrity aspect which is never far from the heart of any of Fuller’s inventions in geodesics. In the present instance, it arises from the concept of using tension rings which grasp the adjoining panels around the circular openings and draw the panels together into a comprehensive tensile network.
132 Once more there is the striking simplicity of componentation. With the use of only two primary panel types, panels twenty feet in diameter will produce a dome or sphere 182 feet in diameter. Fuller said, ‘‘If we reduce the maximum diameter of the components to 10 feet for practicable delivery by truck, the Infrequency layout will permit construction of a dome 88 feet in diameter at the ‘equator.’ Similarly, a 24-frequency layout, using only four main types of components, will permit construction of a dome 176 feet in diameter whose components are of a size to be delivered by conventional motor transport.’’ Thus the mathematics, however profound, find final expression in the most practical results, with even this careful attention to the feasibility of ordinary motor transport to the building site. This characteristic linking of the most sophisticated of mathematical concepts to an awareness of how such concepts can be utilized to man’s greatest advantage, furnishes another indication of Fuller’s concern with the totality of a problem.
133 IN the octet truss, Fuller had projected his ideas for tensile gain in architecture beyond the domical form, as the truss was useful for any other form of building as well. Nine years later, he invented another kind of structure that would, with equal facility, make a building that is round or square, tall or flat, a floor or roof, a tower—or, if one wished, a form like a tree. Or just a ‘‘no’’ form that is unlike anything on earth. This was the star tensegrity of 1964, called simply ‘‘octahedral building truss.’’ The term ‘‘star’’ derived from the star-like facets of a dome designed and built for a country club in the environs of Tokyo.
134 Fuller introduced his invention with an analysis of the history of the art of building that after so many long centuries had not reached the point of more than a token tapping of resources in tensile strength of materials. With care, he outlined the whole problem, noticing the immensity of man’s neglect of his own discoveries of how to make materials stronger in tension:
135136Advances in the technology of materials have resulted in the discovery of the means for producing remarkable increases in tensile strength properties of the materials. Noticeably this has been true in the field of metal alloys, ferrous and nonferrous. Materials of great tensile strength have been developed also in plastics. Glass fibers of enormous strength have become available and are widely used. Notwithstanding the general availability of such high tensile properties in materials, comparatively little has been done in the direction of utilizing pure tension elements in building construction. For building purposes, engineers have clung tenaciously to age-old concepts which rely primarily upon the compressive strength of the materials used so that structures have been erected stone upon stone, beam upon column, all with the utilization of a vast deadweight of materials. With the use of the somewhat lighter weight girders now employed, for example, in the construction of floors and roofs of conventional buildings, some increase in the use of the tensile properties of materials has been made, but still relying to a great extent on the presence of large and heavy compression members.
137 So, said Fuller,
138139I have found a way of building a truss which allows the use of many elements loaded purely in tension, indeed, one in which such purely tensioned elements predominate, so that relatively few compression members are needed. Further, I have discovered how to do this in a way which provides a smooth surface well adapted to cladding in the construction of floors, roofs and walls, and which is remarkably well adapted to the construction of spherical form buildings inclusive of buildings known as geodesic domes.
140 How predominant the tension elements were, is shown by the fact that the basic building ‘‘block’’ of the invention18 was a unit of octahedral form having twelve flexible edges capable of being stressed only in pure tension, and just three columnar members to act under compression. Fuller explained:
142143Regarding the fundamental purpose of the invention, it is, of course, of the utmost significance that we have here a ratio between pure tension and pure compression of four to one. (If when six units are interconnected .. . only one set of tension elements is used where the congruent faces are found, some of the tension elements will be eliminated and the ratio between tension and compression elements will become three to one.) Four to one or three to one as the case may be, the ascendancy of tension to the throne occupied for so long by King Compression is high drama. At long last, builders can begin to realize on the tension potential of a dynamic universe. And it is a universe whose destiny is shaped by the invisible tension network which holds the planets to their celestial orbits. What a pleasing harmony of nature Fuller found in this discovery of a geometrical network of tension that can hold a building erect. Such is the larger frame of reference for the mind of the comprehensivist, Buckminster Fuller.