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Description July 7, 1964 R. B. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 Sheets-Sheet l t 'z n ;:t IN VEN TOR. RICHARD BUCKMINSTER FULLER AT KY5. y 7, 1954 R. a. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 Sheets-Sheet 2 IN V EN TOR. RICHARD BUCKMINSTER FULLER ATT NEYS. July 7, 1964 FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24. 1961 8 Sheets-Sheet 3 IN V EN TOR. RICHARD BUCKMINSTER FULLER y 7, 1954 R. B. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 sheets-Sheet 5 E uvvqvfie'. m5 RICHARD BUCKMINSTER FULLER July 7, 1 4 R. B. FULLER susvmsrou BUILDING 8 Sheets-Sheet 6 Filed Jan. 24, 1961 INVENTOR. RICHARD BUCKMINSTER FILLER AT 0mm. July 7, 1964 R. B. FULLER 3,139,957 SUSPENSION BUILDING Hulk nai N VEN TOR. ATTORNEYS. RIWARD BUCKMINSTER FULL R United States Patent 3,139,957 SUSPENSION BUILDING Richard Buckminster Fuller, 407 S. Forest St., Carbondale, Ill. Filed Ian. 24, 1961, Ser. No. 88,245 11 Claims. (Cl. 189-1) My invention relates to building construction. Summary 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. My new structure comprises a series of box frames of polygonal, cylindrical or other form, these frames being of progressively varying sizes arranged in a concentric array at sequentially different heights above a common plane of reference and in vertically overlapping spaced relation to one another. Tension elements such as flexible cables or wires extend between and are secured to adjacent pairs of the box frames in the series. These tension elements include tension members extending downwardly from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair. In this manner, successive frames of the series are suspended one from another in either a rising, descending or level series as may be desired. Other tension members extend upwardly from their points of securement to one frame of a pair of their respective points of securement to the other frame of a pair whereby successive frames in the series are anchored down one to another. The suspension members and anchor members complement one another in performing a third function, the provision of a tensioned buttress against tilting of the compression members comprised in the frames. Thus are satisfied the three functions of 1) suspension, (2) anchoring and (3) buttressing, all by the simplest arrangement of tension wires in combination with the series of frames as disclosed. Additionally, these tension wires act to stabilize the frames themselves, and furnish a tension system efficiently disposed for resisting torquing and counter-torquing of the frames about the central axis of the structure. These can be catalogued as functions (4) and (5). Still other tension members may be provided that will be disposed in radial planes containing the central axis of the structure. In the case of a structure utilizing a series of frames of polygonal form, the several tension members are secured to the vertexes of the polygons. Those tension members lying in radial planes will apply tension forces to the upper peripheries of the frames and thereby reduce compressive forces imposed on such peripheries by others of the tension mem bers. Description With reference to the drawings I shall now describe the best mode contemplated by me for carrying out my invention. FIG. 1 is an elevational view partly in vertical section illustrating the application of my invention to a roofed stadium or concert hall. 3,139,957 Patented July 7, 1964 ice FIG. 2 is a plan view of the FIG. 1 structure with the right-hand portion of the roof covering removed to reveal the suspension frame construction, taken as indicated at 2-2 in FIG. 1. FIG. 3 is an elevational view illustrating another embodiment of the invention, the right-hand portion being shown in diagrammatic vertical section. FIG. 4 is a similar view of another embodiment. FIG. 5 is a plan view of the suspension frame system of the FIG. 4 structure, taken as indicated at 5-5 in FIG. 4. FIG. 6 is a diagrammatic vertical section of a still further embodiment of the invention. FIG. 7 is a plan view of the FIG. 6 structure, roof covering omitted, taken as indicated at 7--7 in FIG. 6. FIGS. 8 to 17 inclusive are diagrammatic representations illustrative of the general scope of applicability of my suspension building system to various building forms with the use of different kinds of box structures and with several alternative dispositions of the suspension and anchoring cables, FIG. 8 being a vertical sectional view illustrative of flanged cylindrical box sections, FIG. 8a a plan view illustrative of an asymmetrical form of my construction, FIG. 9 a vertical sectional view illustrative of flanged box sections of frusto-conical form, FIG. 10 illustrative of the use of similar box sections of inverted frusto-conical form, FIG. 11 a plan view illustrative of a special elongated form of box section, FIG. 12 an isometric perspective view of another form of framing and one alternative arrangement of the suspension and anchoring cables, FIG. 13 a diagram analyzing the vertical components of the reach of the cables of FIG. 12, FIG. 14 a partial view similar to FIG. 12 with an alternative disposition of the cables, FIG. 15 a diagram analyzing the vertical components of the reach of the cables of FIG. 14, FIG. 16 a view similar to FIG. 14 showing a still further disposition of the cables, and FIG. 17 a diagram analyzing the vertical components of the reach of the cables of FIG. 16. FIG. 18 is a perspective view illustrating the application of my invention to a spherical or hemispherical structure based on the spherical octahedron. FIG. 19 is a detail cross-sectional view taken on the line 1919 of FIG. 18. In FIGS. 1 and 2 we see a structure embodying my invention in one of its preferred forms as applied, for example, to a roofed sports arena or stadium. The structure comprises a series of polygonal box frames 1 to 10 inclusive, 2, 3 and 4. In this particular construction each frame is comprised of upper chord members 11 and lower chord members 12 forming the upper and lower peripheries of the respective frames, and vertical compression columns or struts 13 extending between the vertexes of the polygon formed by the upper chord members 11 and the corresponding vertexes of the polygon formed by the lower chord members 12. Considering an individual frame as a whole, such frame is an annular form faceted into rectangles around its rim or periphery by the members 11, 12 and 13. The series of box frames 1 to 10 inclusive, 2, 3 and 4, are of progressively varying sizes and they are arranged in a concentric array at sequentially different heights above a common plane of reference (for instance, the horizontal plane of the foundation) and in vertically overlapping spaced relation one to another. Tension elements extend between and are secured to adjacent pairs of the box frames in the series, these tension elements including tension members 3 14, 14' which extend downwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are suspended one from another [function (1) of the Summary given at the beginning of this specification]. The tension elements also include other tension members 15, 15' extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another [function (2) of the Summary]. Tension members 14 and 15 may be arranged in crisscrossing pairs as shown in FIG. 2. In this particular embodiment the same tension members are crisscrossed whenviewed in plan, FIG. 2, as well as when viewed in elevation. The downwardly extending tension members may include members disposed in radial planes containing the central axis 16 of the structure, and the upwardly extending tension members 15 also may include members disposed in such radial planes. In FIG. 1 the particular tension members 14' and 15' which come into view are those which lie in one of such radial planes. In the preferred construction shown, the several tension members 14, 15, 14', 15 are secured to the respective polygonal box frames at the vertexes thereof. Also in this particular construction the domical structure formed by the series of suspended box frames is flattened on top by the provision of a series of box frames 10, 17 and 18 of progressively varying sizes arranged in a concentric array above the common horizontal plane of reference and in horizontally spaced relation one to another. As in the rest of the structure, we have the tension members 14, 14' functioning as suspension members, and 15, 15 functioning as anchoring members. All such tension members 14, 14', 15, 15' complement one another in performing a third function, the provision of a tensioned buttress against tilting of the compression members 13 comprised in the frames [function (3) of the preceding Summary]. Additionally, these tension members act to stabilize the frames themselves and furnish a tension system efiiciently disposed for resisting torquing and counter-torquing of the frames about the central axis 16 of the structure [functions (4) and (5) of the Summary]. Further, the tension members 14', 15' which extend outwardly from the upper and lower peripheries of the frames will apply tension forces which will reduce compressive forces imposed on such peripheries by others of the tension members. Annular frames 1 to 10 inclusive are illustrative of a rising series of frames, annular frames 1, 2, 3 and 4 illustrative of a descending series of frames, and annular frames 10, 17 and 18 illustrative of a level series. The level series may terminate in a single central strut or annulus 19. Beginning at the base of the structure we have the annular frame 4 from which is suspended at a higher elevation the frame 3 from which in turn is suspended the frame 2 and then in succession we have suspended each from the other in the order named the frames 1, 2, 3 and so on, altitude being gained meanwhile in the progressively stepped suspension system. Similarly, frame 17 is suspended from frame 10, frame 18 from 17, and center post 19 from frame 18. As in the suspension bridge the tension aspect of the structure is highly significant through utilization of the more favorable tensile strengths of materials as contrasted with their vastly inferior compressive strengths. It would be difficult to imagine an upside down suspension bridge and yet that is in effect what I have achieved when my structure is considered in any given vertical profile. Altitude is gained by breaking up the suspension systeminto steps and stability of the stepping is attained by the three dimensional aspect of the structure as contrasted with the essentially two dimensional system of the suspension bridge. The end result is a tremendous saving through the realization of a larger building per unit weight of the material employed in its construction, this in turn being the benefit conferred by my discovery of how to get more use from the most favorable property of materials, namely tensile strength. Essentially I have devised a building construction which in large measure replaces heavy columns and beams with a light spidery array of tension wires or cables. The structure can be roofed in many ways. In the embodiment of FIGS. 1 and 2, roofing sheets 20 of trapezoidal form are shown. The method by which these are attached and the detail of their construction are not an essential part of my present invention. In FIG. 3 I have shown a modified frame construction in which the compression members 21, 22, etc. are comprised of elliptical struts designed for increased efficiency in the use of materials in compression. Pagoda roofing is here employed to advantage as an eificient watershed with provision for good ventilation by means of windows or louvres 54 set well under the overhangs in the roof. In FIGS. 4 and 5 the polygonal frames comprise a series of diamond shaped frames 24 to 27 inclusive. Suspension wires 28, 28' suspend each successively higher frame from the lower-numbered frame of the series. Anchoring wires 29, 29 disposed in radial planes containing the central axis of the structure are provided as before. Both the wires 28, 28' and the wires 29, 29' are secured to the upper edge of the lower frame of each pair of frames, in this respect representing a variation from the crisscrossing arrangment of FIGS. 1 and 2. The roof structure here simplifies into a generally pyramidal form. It is essential to understand that the box or annular frames of my invention may be either skeletal as when made of strust or tubes as I have described, or continuous as when made in the form of sheets, plates or panels. In FIG. 8 we see an example of the latter construction in which the frames or annuli are comprised of simple cylinders 30, 31 and 32. These may have marginal flanges 33 as shown. In the embodiment typified here the suspension wires 34 extend downwardly from the upper edge of the lower frame of a pair to the lower edge of the upper frame of the pair, and the anchor cables 35 extend from the lower edge of the lower frame of a pair to the lower edge of the upper frame of the pair (instead of to the upper edge of the pair as in the embodiment of FIGS. 1 and 2). The system of wires 35 may be projected as at 36 if desired, providing a continuous line of tension from the top to the base of the structure. FIG. 8a shows the application of my invention to an asymmetrical structure comprising the frames 37, 38, 39, 53, which may be of any desired peripheral contour. FIG. 9 represents another kind of continuous annular frame 40, 41, 42, being one of frusto-conical form. In FIG. 10 the frusto- conical frames 43, 44, 45 are inverted from the position of those in FIG. 9. If the sheet containing FIGS. 8, 9 and 10 is inverted, we see three additional variants in which either cylindrical or frusto-conical frames are arranged in what I have previously referred to herein as a descending series. This would equate to the series 2, 3, 4 in FIG. 1. FIG. 11 shows the application of my invention to an elongated structure of involute-evolute form comprising end sections 46, 47, of generally hexagonal pyramidal form and a connecting section of involute-evolute form, affording added strength to such an elongated structure. The disposition of the suspending-anchoring-buttressing cables may be generally similar to that in the structures already described. The construction of the frames themselves as seen in elevation will be generally similar to that described with reference to FIG. 1. FIGS. 6 and 7 shows the application of my invention to a structure of hexagonal form comprising the series of hexagonal frames 49, 50, 51, 52, each higher-numbered frame being suspended from the lower-numbered frame of the series. Here the extent of vertical overlapping between successive frames varies whereas the horizontal spacing remains contsant. This is incontradistinction to the arrangement of FIG. 1 in which the horizontal spacing between successive frames varies. The feasibility of varying both vertical overlap and horizontal spacing lends great flexibility to the design of the structure. FIG. 12 shows the application of my invention to a rectangular form of structure comprising the series of rectangular frames 55, 56, 57. As before, these frames can be considered to be made up of struts in an open or skeletal framework or to be continuous as when made in the form of sheets or panels. The frames themselves may if desired be triangulated through the use of diagonal wires extending between the diagonally opposite corners of each side or facet of the frame. FIG. 13 may be considered as a diagrammatic section taken either on the central diagonal plane or a central plane bisecting the sides of the frames, s being the suspension members and a the anchoring members. Regarding FIG. 13 as the diagonal section, s and a are both disposed in a vertical plane containing the axis of the structure. Regarding FIG. 13 as the section bisecting the sides of the frames, s and a are crisscrossed both horizontally and vertically as will be understood from FIG. 12. In either case FIG. 13 gives a picture of the vertical components of the reach of the cables. FIGS. 12-13, FIGS. 14-15 and FIGS. 16-17 are comparative views illustrative of the general scope of applicability of my suspension building system to structures utilizing several alternative dispositions of the suspension and anchoring cables. FIGS. 14 and 16 represent portions of the same frame arrangement shown in FIG. 12 but the arrangement of the tension members is different. The difference in this arrangement may best be discerned in FIG. 15 as compared with FIG. 13. In FIG. 15 suspension cables .9 extend in the same manner as the cables s of FIG. 13 but the anchoring cables a extend between the upper corners of the successive frames in the series. FIGS. 16 and 17 shows another alternative arrangement of the tension members in which the anchoring cables a" extend between the lower comers of the successive frames in the series. Thus in the construction of FIGS. 12-13 we have vertically crisscross cables whereas in FIGS. 14-15 and FIGS. 16-17, these cables do not cross one another although the tensioning pattern in all cases is triangulated, resulting in an omni-triangulated building construction. The differing patterns of triangulation may be combined in various ways, using one system at one side or facet of the structure and an alternate system in the adjacent side as may be desired. Another alternative arrangement would be to use only suspension elements s, s or s" at one side of the series of frames and only anchoring elements a, a or a" in the side adjacent and continuing this alternating suspension and anchoring in succeeding sides. FIGS. 18 and 19 show the application of my invention to a spherical structure or to a segment of a spherical structure based on the spherical octahedron. Here we have a hemispherical dome comprising four spherical triangles of the octahedron defined by the intersections of three great circles 58, 59, 60. Relating these to the globe we have the great circle 58 at the equator, 59 at 0 and 180 longitude, and 60 at 90 and 270 of longitude. Two of the spherical triangles of the octahedron appear at 61 and 62. Each is subdivided by means of any selected number of spherical triangles of progressively smaller sizes arranged in a concentric array. These several concentric triangles form the inner or outer edges of frames of either skeletal or continuous form. Considering the frame array for spherical face 61 of the octahedron, we have the frames 63, 64, 65, 66. Considering the several frames of the series to be of the same radial depth (67=68=69=70), and reorienting the structure so that a line containing the center of spherical face 61 and the center of the sphere is vertical, we have, as in other forms of my invention, a series of box frames of progressively varying sizes arranged in a concentric array at sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another. Also, as before, tension elements 71, 72, FIG. 19, extend between and are secured to adjacent pairs of the frames in the series. Tension elements 71 extend downwardly, i.e. inwardly of the sphere, from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair whereby successive frames in the series are suspended one from another. Tension members 72 extend upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down, i.e. inwardly of the sphere, one to another. It will be understood that the several tension elements serve all of the five functions described hereinabove, namely those of suspension, anchoring, buttressing, stabilizing of the frames themselves and resisting torquing and countertorquing of the frames about a line passing through the centers of the sphere and of the octahedral face. It may be mentioned that in FIG. 18 I have for simplicity of illustration omitted tension elements 71 and 72, the general arrangement of which will be understood from the description of the other forms of my invention. Also, it will be understood that any of the described alternate arrangements of the tension elements may be employed as desired. The terms and expressions which I have employed are used in a descriptive and not a limiting sense, and I have no intention of excluding such equivalents of the invention described as fall within the scope of the claims. I claim: 1. A structure comprising a series of box frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair of their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 2. A structure according to claim 1 in which said tension elements also include other tension members extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another. 3. A structure comprising a series of cylindrical frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the cylindrical frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby succesive frames in the series are permanently suspended one from another in predetermined fixed positions. 4. A structure comprising a series of polygonal box frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the polygonal box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 5. A structure according to claim 4 in which said tension elements also include other tension members extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another. 6. A structure according to claim 4 in which said downwardly extending tension members include members disposed in radial planes containing the central axis of the structure. 7. A structure according to claim 6 in which said downwardly extending tension members are secured to tle respective polygonal box frames at the vertices there- 8. A structure comprising a series of frusto-conical frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the frusto-conical frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 9. A structure comprising a series of box frames of progressively varying sizes arranged in a concentric array above a common horizontal plane of reference and in horizontally spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to one frame of a pair to their respective points of fixed securement to the other frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 10. A structure according to claim 9 in which said tension elements also include other tension members extending upwardly from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair whereby successive frames in the series are anchored down one to another. 11. A structure according to claim 10 in which said downwardly extending tension members include members disposed in radial planes containing the central axis of the structure. References Cited in the file of this patent UNITED STATES PATENTS 2,576,389 Craighead etal Nov. 27, 1951 2,621,765 Wood Dec. 16, 1952 2,689,025 Yates Sept. 14, 1954 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 139.957 July 7, 1964 Richard Buckminster Fuller It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patentshould read as corrected below. I Column 1, line 41, for "of", second occurrence. read e Signed and sealed this 10th day of November 1964. (SEAL) Attest: ERNEST W. SWIDER Allcsting Officer EDWARD J. BRENNER Commissioner of Patents

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Description Nov. 28, 1967 FU 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 1 Hll'inll I NVENTOR. 03 g RICHARD BUCKMINSTER FULLER TT EYS. Nov. 23, 1967 R, B, FULLER 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 5 I N VE NTOR. RICHARD BUCKMINSTER FULLER 1967 R. a. FULLER 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 4 -INVENTOR. RICHARD BUCKMINSTER FULLER ATT NEYS. 1967 R. B, FULLER 3,354,591 7 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 t 6 Sheets-Sheet 5 DEED ' INVENTOR. If 11 IE: 0 Hz H 11 B RICHARD BUCKMINSTER FULLER BY 7%.A', ,1 OCTAHEDRAL BUILDING TRUS 5 Filed Dec. 7, 1964 6 Sheets-Sheet 6 I NVENTOR. RICHARD BUCKMINSTER FULLER A770 EYS. United States Patent 3,354,591 OCTAHEDRAL BUILDING TRUSS Richard Buckminster Fuller, 407 S. Forest St, Carbondale, Ill. 62901 Filed Bee. 7, 1964, Ser. No. 416,228 12 Claims. (Cl. 52-81) The invention relates to a building truss particularly adapted to the construction of geodesic domes and having special advantages for use in other kinds of structures as well. Advances 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 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. Summary It has been a primary object of my invention to provide a truss construction which is capable of utilizing more efficiently the tensile strengths of the materials from which the truss is constructed. I 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. A particular characterizing feature of my present invention resides in putting together in a new way a plurality of units of octahedral formeach having eight triangular faces, such units being connected face to face so that each pair of adjacent units have one face thereof in congruity. In the preferred form of my truss, each of the interconnected units comprises twelve flexible members capable of being stressed only in pure tension and three compression elements consisting of criss-crossed stiff members capable of being loaded as compression columns. Regarding 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 in the manner shown in FIG. 3, only one set of tension elements is used where the congruent faces are found, some of the tension elements will be leiminated and the ratio between tension and compression elements will become three to one.) Yet, as will be explained hereinbelow, this predominance of tension elementswhich can even be slender wires or cables-is accomplished in a way to provide a smooth planar or spherical surface for cladding in a most convenient manner. Description 'moved to reveal a portion of the underlying truss. FIG. 3 is a view similar to FIG. 2 but with all of the cladding elements removed to reveal all of the elements of the truss. FIG. 4 is a fragmentary cross sectional view taken generally as indicated at 44 in FIG. 1, the scale being somewhat enlarged. FIG. 5 is a detail view of one of the six octahedral units which together make up the truss section of FIG. 3. , FIG. 6 is a. view similar to FIG. 5 illustrating a modified form of the octahedral unit. FIG. 7 is an exploded view ofone pair of octahedral units used in the FIG. 3 truss. FIG. 8 is a top perspective view of a six-sided capping member which forms a part of the cladding shown in FIG. 2. FIG. 9 is a top perspective view of a triangular capping member which forms another part of the cladding shown in FIG. 2. FIG. 10 is a diagram showing the relationship between several types of elements which can form a part of a geodesic dome constructed in accordance with the invention. FIG. 11 is a view similar to FIG. 4, showing a modified construction. FIG. 12 is a side elevational view of a mast structure embodying my invention in another form. FIG. 13 is a view similar to FIG. 12, showing a modified form of mast structure. FIG. 14 is a view illustrating an application of the invention to a structure of assymmetn'ca-l form. FIG. 15 is a perspective view, partially exploded, showing elements of two associated octahedral units constructed in accordance with another embodiment of the invention. With reference to FIG. 5, I shall first describe one of the octahedral building blocks which form the basic unit of the construction. It has eight triangular faces and is, therefore, an octahedron. The eight triangular faces are defined by the tension elementswhich normally will be made of flexible wires or cables. The-re are three compression elements, 4, 5, and 6, which are arranged along the three axes of the octahedron, 1-1', 2-2 and 33'. In reading FIGS. 3, 5, 6 and 7, it will be helpful to note the following: The reader is looking top down on the truss and truss units. The upper ends of the compression sion members 4, 5 and 6 so that they will appear larger at the end near to the reader. Interconnection of adjacent units in face to face relationship will be understood from FIG. 7 in which two adjacent units have been drawn apart slightly. When brought together, the faces 1'23 of the two units shown will be congruent. In the unit which appears in the lower part of FIG. 7, the tensile lines .1'-2, 23, and -3 1'-3' have been shown as imaginary lines, for when the two units are brought together the tension elements 1'2, 23 and 13' of the upper unit can serve as common tension elements of the two associated units as may in some cases be desired. In FIG. 3 we see six associated octahedral units of FIG. 5, each adjacent pair of such units being interconnected in the manner I have described with reference to FIG. 7. The interconnected units form a trus structure comprising a network of tension elements arranged in a patter-n defining a plurality of the FIG. octahedra in face to face relationship as depicted in FIG. 7. A compression member 4, 5 or 6 extends between each of the three opposed pairs of vertexes of each octahedron. This description of my construction may now be summarized more simply as a truss structure comprising tension elements defining octahedra arranged face to face, and compression elements arranged along the three axes of each octahedron. The seemingly complex but truly simple forms of the octahedral units will be further understood by identifying the faces of the octahedra, the tension elements and the compression elements as follows: Eight faces of the octahedra: Three compression elements: From the foregoing tabulation of the truss elements, the student of this disclosure will appreciate the preponderance in tension elements over compression elements and the significant improvement thus obtained in the direction of increased utilization of the high tensile properties of the improved materials and alloys available today. The problem heretofore has not been the availability of materials of good tensile properties, but rather the ques tion of how such properties could be utilized more fully in the realm of building architecture; and how this could be done in a practical manner which would provide surfaces which could conveniently be cladded-eveu though such surfaces seem to be made up of a maze of wires and to be inherently spikey. How this can be done is now further disclosed with more particular reference to FIGS. 2, 4, 8 and 9 of the drawings: If we take a truss section of the extent comprised of six associated octahedra, it will be noticed that one face (1-2-3) of each of the six octahedra lies in a common surface. These faces of the six octahedral units are joined together vertex to vertex, and together encircle a hexagonal area. The six triangular faces 123 are enclosed by triangular capping members 8 which may be secured in any convenient manner as by bolting them to fittings 1, 2 and 3, FIG. 5, which may be apertured as at 9, FIG. 3, to receive bolts passin through aligned apertures 10 in overlapping corner portions of the triangular capping members. By this means, the capping members are secured to each other and to the underlying truss. In the preferred construction shown, the triangular capping members 8 are formed as panels having upwardly extending marginal flanges 11, FIG. 9. The hexagonal area within the circle of triangular panels 8, FIG. 2, may then be enclosed in any suitable manner. This may be done most advantageously with the use of a hexagonal capping member 12, FIG. 8, having downwardly extending marginal flanges 16 which fit over the upwardly extending flanges 11 at the edges of the hexagonal area. The hexagonal capping member 12 is advantageously formed with three adjoining diamond-shaped surfaces 13, 14, and 15 of hyperbolic-paraboloid form. Various materials may be employed in the cladding of the structure including formed or molded sheets of steel, aluminum, plastics, fiberglass or other suitable materials. In the representative construction shown, the triangular capping members 8 are made of steel and the six-sided capping members 12 are made of fiberglass-reinforced polyester resin. In the construction shown in FIG. 8,- this capping member is further reinforced along the ridges formed by the adjoining edges of the hyperbolic-paraboloids by hollow molded ribs 17 filled with a urethane foam 18. (The cladding construction which I have described forms an effective watershed by reason of the interlocking flanges of the several cladding members and the arrangement by which the water can flow from one triangular panel to another. These panels together form a maze of gutters which will serve to clear a heavy flow of rainwater.) In FIG. 6, I have illustrated a modified form of the fundamental octahedral unit in which the compression members extending between each of the three opposed pairs of vertexes 1-1, 22' and 3-3 of the octahedron are each made in two parts joined together centrally of the unit by a hub member 7 provided with three pairs of fittings aligned with the respective axes of the compression members. It will be observed that in the embodiment shown in FIG. 5, the compression members 4, 5 and 6 are arranged to bypass one another in the manner of the poles of a tepee. At the point of bypass, the members may be spaced from one another or be in contact. They may or may not be secured to one another at the point of bypass as desired. In the embodiment of FIG. 6, the compression members can be arranged so that their axes intersect, the single members 4, 5 and 6 here being replaced by the compound compression members ill-4b, 5a5b, 6a6b, respectively. When my invention is utilized in geodesic dome construction, some of the octahedral units will be arranged so that their triangular capping members encircle a pentagonal area as distinguished from the hexagonal area described with reference to FIGS. 2 and 3. This occurs at each vertex of the icosahedron, dodecahedron or tricontahedron on which the design of the geodesic dome is based. This aspect of geodesic construction is well known to architects familiar with such construction, and will be understood from the disclosure of my fundamental geodesic building construction Patent No. 2,682,235 where the pentagonal areas can be seen clearly in FIGS. 1 and 2. Thus in a geodesic dome constructed in accordance with my present invention, some of the octahedral units are arranged so that one face of each of six associated units lies in a common spherical surface, such faces of the six associated units being joined together vertex to vertex and enclosed by triangular capping members which encircle a hexagonal area in the common spherical surface, such hexagonal area being enclosed by a six-sided capping member adjoining each of the six triangular capping members; whereas, others of the octahedral units are arranged so that their triangular capping members encircle a pentagonal area in the commonspherical surface, such pentagonal area being enclosed by a five-sided capping member adjoining each of the five triangular capping members. This will be further understood from the diagram of FIG. 10. The area covered by this diagram can be compared with the ,area at the zenith Z of my geodesic patent aforesaid. Triangular capping members T, T1, T2, T3, H4, T5 encircle a hexagonal area which is enclosed by a six-sided capping member H which might, for example, be of the construction which has been described with reference to FIG. 8. Triangular capping members T, T1, T6, T7, T8 encircle a pentagonal area enclosed by a five-sided capping member P. Capping member P may be of simple pyramidal form ,as distinguished from the hyperbolic-paraboloid form of FIG. 8, or H in the diagram. Further, the form of the six-sided capping members may be modified according to the wishes of the architect; for example, they may be of the simple pyramidal form shown at H1 in the diagram. FIG. 11 illustrates a further development of the construction of FIG. 4, in which the proportions of the octahedral units are altered to create a flat floor or roof truss. This truss is then built up into two or more thicknesses (two as shown) in which every other truss is inverted. Here the smaller faces 1-2-3 of the two trusses are joined congruently. Similarly, two trusses may be joined in a manner which brings the larger faces 123' into congruent relation. FIG. 12 illustrates the application of my invention to a mast or tower structure. In this case the opposed faces 123 and 1'2'3 of the octahedrons are of the same size, and parallel to one another. FIG. 13 illustrates a modification of the FIG. 12 structure in which opposed faces 1-23 and 1' 3' are of different size, and are not parallel to one another. FIG. 14 illustrates an application of my invention to an asymmetrical structure which reveals the comprehensive adaptability of my invention to structures of irregular form. The octahedrons A, B, C, D, etc., can be varied in their relative proportions and shapes, grouped and extended as desired, while availing of the favorable weightstrength ratio obtained by reason of the preponderance of tension elements over compression elements. FIG. 15 illustrates a further modification of the octahedral units in which the twelve edges of each octahedron are in the form of structural shapes such as the angle irons of steel or aluminum shown at 19. Vertex members 1a, 2a and 3a correspond to members 1, 2 and 3 of FIGS. 5, 6 and 7. These are advantageously made as metal castings to which the structural shapes 19 are welded as 20. The construction thus comprises a plurality of interconnected units each of which comprises twelve members interconnected to form the edges of a self-supporting unit having eight triangular faces, the units being connected face to face so that each pair of adjacent units have one face and three members thereof in congruity. The faces which are connected in congruity are those which are shown spaced slightly apart, these faces being designed to be bolted together in the manner indicated by the exploded bolting elements, which pass through aligned apertures in the congruent edge members. In each of the embodiments described, my structure comprises a plurality of interconnected units each of which includes twelve members interconnected to form the edges of a figure having eight triangular faces, an outer face of the several units lying in a common surface and an inner face of the several units lying in a second common surface spaced from and parallel to the first. For example, in the embodiment of FIGS. 1-5 and 7, and with particular reference to FIG. 5, we have an outer face 1-2-3 and an inner face 1'23', these two faces lying in surfaces which are spaced from and parallel to one another. Notice that the outer face 1-2-3 is approximately one-half the size of the inner face 1'2'-3 and that the two faces are so oriented relative to one another that the vertices of the outer face lie substantially above the midpoints of the sides of the inner face. Above is used here in the sense of beyond or outside of; and it will be understood that if the truss extends in a generally horizontal direction, vertex 2, for example, of the outer face 12-3 will lie above the side 1'2'3' of the inner face 12-3', whereas, if the truss is located so as to extend in a generally vertical direction, vertex 2 will be beyond or outside of side 13'. If the inner and outer surfaces of the truss are parallel fiat planes arranged horizontally, vertex 2 will be directly above side 1-3. Again, if the common surfaces are concentric spherical surfaces, ver tex 2 will be disposed radially outside of the midpoint of side 1'3'. So in all cases it can be considered that the orientation of the outer and inner faces of each unit is such that the vertices 1, 2, and 3 of the outer face lie substantially above the midpoints of the sides of the inner face 1'2'-3'. The relative size and orientation of the inner and outer faces of each unit as described in the preceding paragraph makes it possible to interconnect the several units in a manner which joins the outer faces together vertex to vertex and which joins the inner faces together edge to edge. If the truss is inverted or turned inside out, the inner faces will be joined together vertex to vertex and the outer faces edge to edge. The terms and expressions which I have employed are used in a descriptive and not a limiting sense, and I have no intention of excluding equivalents of the invention described and claimed. I claim: 1. A truss structure comprising a network of tension members and compression members; the tension members being joined in three opposed pairs of junctions, the junctions of the tension members forming vertices lying in planes defining an octahedron, said tension members of adjacent octahedra being connected, with the connections therebetween defining a common plane of said adjacent octahedra, and said compression members extending between each of said three opposed pairs of junctions of said tension members of each octahedron. 2. A truss structure comprising a network of tension members and compression members; the tension members being joined in a multiplicity of three opposed pairs of junctions, the junctions of the respective tension members forming three opposed pairs of vertices lying at the vertices of eight triangular faces defining an octahedron, said tension members of adjacent octahedra being connected, the adjacent octahedra being positioned with a triangular face of one in face to face relationship with a triangular face of another, the connections between adjacent octahedra defining a first and a second common surface, one of the triangular faces of each octahedron lying in said first common surface and another of the triangular faces of each octahedron lying in said second common surface, and three of said compression members being positioned in criss-crossed relationship and extending between each of said three opposed pairs of junctions of each octahedron. 3. A truss structure for a geodesic dome comprising a plurality of interconnected self-supporting units each of which comprises twelve members interconnected at six junctions forming vertices of the respective units and with said twelve members forming the edges of the respective units, each unit having eight triangular faces, said units being connected face to face so that each pair of adjacent units have one face and three members thereof in congruity. 4. A truss structure in accordance with claim 3 in which one face of each of six associated units lies in a common spherical surface, said faces of said six associated units being joined together vertex to vertex and each being closed by respective ones of six triangular capping members which encircle a hexagonal area in said common spherical surface, said hexagonal area being enclosed by a six-sided capping member adjoining each of the six t-riangular capping members. 5. A truss structure in accordance with claim 3 in which one face of each of six associated units liesin a common spherical surface, said faces of said six associated units being joined together vertex to vertex and each being closed by respective ones of six triangular capping members which encircle a hexagonal area in said common spherical surface, said hexagonal area being enclosed by a six-sided capping member adjoining each of the six triangular capping members, said six-sided capping member being formed with three adjoining diamond-shaped surfaces of hyperbolic-paraboloid form. 6. A truss structure in accordance with claim 4 in which one face of each of five other associated units lies in said common spherical surface, said faces of said five associated units being joined together vertex to vertex and being closed by respective ones of five triangular capping members which encircle a pentagonal area in said common spherical surface, said pentagonal area being enclosed by a five-sided capping member adjoining each of the five triangular capping members. 7. A truss structure comprising a plurality of interconnected units each of which includes twelve members interconnected at six junctions forming six vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each having eight triangular faces including an outer face and an inner face, the outer face of the respective units lying in a common surface and the inner face of'the respective units lying in a second common surface spaced from and parallel to the first, said outer faces being approximately one-half the size of said inner faces and the outer and inner faces of each unit being so oriented relative to one another that the vertices of the outer face lie substantially above the mid-points of the edges of the inner face, the respective units being interconnected in a manner which joins the outer faces together vertex to vertex and the inner faces edge to edge. 8. A truss structure according to claim 7 in which said first and second common surfaces are parallel flat planes. 9. A truss structure according to claim 7 in which said first and second common surfaces are parallel curved surfaces. 10. A truss structure according to claim 7 in which said first and second common surfaces are concentric spherical surfaces. 11. A truss structure comprising a plurality of interconnected units each of which includes twelve members interconnected at six junctions forming six vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each having eight triangular faces including a first face and a second face, the first face of the respective units lying in a common surface and the second face of the respective units lying in a second common surface spaced from and parallel to the first common surface, one of said first and second faces of each unit being approximately one-half the size of the other of said first and second faces, and said first and second faces of each unit being so oriented relative to one another that the vertices of one such face lie substantially opposite the midpoints of the edges of the other such face, the respective units being interconnected in a manner which joins one of said first and second faces of the respective units together vertex to vertex and which joins the other of said first and second faces of the respective units together edge to edge. 12. A truss structure comprising a plurality of interconnected units each of which includes twelve members joined at six junctions forming three opposed pairs of vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each being an octahedral figure having eight triangular faces including a first such triangular face and a second such triangular face, the first such face of the respective units lying in a common surface and the second such face of the respective units lying in a second common surface spaced from and parallel to the first common surface, said twelve members of the respective interconnected units being constituted by fiexible members capable of being stressed only in pure tension and each of said units further including three criss-crossed stiff members capable of being loaded as compression columns, said stiff members extending between each of the three opposed pairs of vertices of the octahedral figure formed by said eight triangular faces. References Cited UNITED STATES PATENTS 2,918,992 12/1959 Gelsavage 52-81 3,058,550 10/1962 Richter 52582 X 3,169,611 2/1965 Snelson 52578 X 3,220,152 11/1965 Sturm 52-81 X FOREIGN PATENTS 1,377,290 9/ 1964 France. 1,377,291 9/1964 France. FRANK L. ABBOTT, Primary Examiner. C. G. MUELLER, Assistant Examiner.

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The 99 Failures Pavilion realised by the University of Tokyo's Digital Fabrication Lab reveals highly immersive structural, material and spatially perceptual experiences.

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Description Nov. 28, 1967 FU 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 1 Hll'inll I NVENTOR. 03 g RICHARD BUCKMINSTER FULLER TT EYS. Nov. 23, 1967 R, B, FULLER 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 5 I N VE NTOR. RICHARD BUCKMINSTER FULLER 1967 R. a. FULLER 3,354,591 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 6 Sheets-Sheet 4 -INVENTOR. RICHARD BUCKMINSTER FULLER ATT NEYS. 1967 R. B, FULLER 3,354,591 7 OCTAHEDRAL BUILDING TRUSS Filed Dec. 7, 1964 t 6 Sheets-Sheet 5 DEED ' INVENTOR. If 11 IE: 0 Hz H 11 B RICHARD BUCKMINSTER FULLER BY 7%.A', ,1 OCTAHEDRAL BUILDING TRUS 5 Filed Dec. 7, 1964 6 Sheets-Sheet 6 I NVENTOR. RICHARD BUCKMINSTER FULLER A770 EYS. United States Patent 3,354,591 OCTAHEDRAL BUILDING TRUSS Richard Buckminster Fuller, 407 S. Forest St, Carbondale, Ill. 62901 Filed Bee. 7, 1964, Ser. No. 416,228 12 Claims. (Cl. 52-81) The invention relates to a building truss particularly adapted to the construction of geodesic domes and having special advantages for use in other kinds of structures as well. Advances 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 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. Summary It has been a primary object of my invention to provide a truss construction which is capable of utilizing more efficiently the tensile strengths of the materials from which the truss is constructed. I 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. A particular characterizing feature of my present invention resides in putting together in a new way a plurality of units of octahedral formeach having eight triangular faces, such units being connected face to face so that each pair of adjacent units have one face thereof in congruity. In the preferred form of my truss, each of the interconnected units comprises twelve flexible members capable of being stressed only in pure tension and three compression elements consisting of criss-crossed stiff members capable of being loaded as compression columns. Regarding 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 in the manner shown in FIG. 3, only one set of tension elements is used where the congruent faces are found, some of the tension elements will be leiminated and the ratio between tension and compression elements will become three to one.) Yet, as will be explained hereinbelow, this predominance of tension elementswhich can even be slender wires or cables-is accomplished in a way to provide a smooth planar or spherical surface for cladding in a most convenient manner. Description 'moved to reveal a portion of the underlying truss. FIG. 3 is a view similar to FIG. 2 but with all of the cladding elements removed to reveal all of the elements of the truss. FIG. 4 is a fragmentary cross sectional view taken generally as indicated at 44 in FIG. 1, the scale being somewhat enlarged. FIG. 5 is a detail view of one of the six octahedral units which together make up the truss section of FIG. 3. , FIG. 6 is a. view similar to FIG. 5 illustrating a modified form of the octahedral unit. FIG. 7 is an exploded view ofone pair of octahedral units used in the FIG. 3 truss. FIG. 8 is a top perspective view of a six-sided capping member which forms a part of the cladding shown in FIG. 2. FIG. 9 is a top perspective view of a triangular capping member which forms another part of the cladding shown in FIG. 2. FIG. 10 is a diagram showing the relationship between several types of elements which can form a part of a geodesic dome constructed in accordance with the invention. FIG. 11 is a view similar to FIG. 4, showing a modified construction. FIG. 12 is a side elevational view of a mast structure embodying my invention in another form. FIG. 13 is a view similar to FIG. 12, showing a modified form of mast structure. FIG. 14 is a view illustrating an application of the invention to a structure of assymmetn'ca-l form. FIG. 15 is a perspective view, partially exploded, showing elements of two associated octahedral units constructed in accordance with another embodiment of the invention. With reference to FIG. 5, I shall first describe one of the octahedral building blocks which form the basic unit of the construction. It has eight triangular faces and is, therefore, an octahedron. The eight triangular faces are defined by the tension elementswhich normally will be made of flexible wires or cables. The-re are three compression elements, 4, 5, and 6, which are arranged along the three axes of the octahedron, 1-1', 2-2 and 33'. In reading FIGS. 3, 5, 6 and 7, it will be helpful to note the following: The reader is looking top down on the truss and truss units. The upper ends of the compression sion members 4, 5 and 6 so that they will appear larger at the end near to the reader. Interconnection of adjacent units in face to face relationship will be understood from FIG. 7 in which two adjacent units have been drawn apart slightly. When brought together, the faces 1'23 of the two units shown will be congruent. In the unit which appears in the lower part of FIG. 7, the tensile lines .1'-2, 23, and -3 1'-3' have been shown as imaginary lines, for when the two units are brought together the tension elements 1'2, 23 and 13' of the upper unit can serve as common tension elements of the two associated units as may in some cases be desired. In FIG. 3 we see six associated octahedral units of FIG. 5, each adjacent pair of such units being interconnected in the manner I have described with reference to FIG. 7. The interconnected units form a trus structure comprising a network of tension elements arranged in a patter-n defining a plurality of the FIG. octahedra in face to face relationship as depicted in FIG. 7. A compression member 4, 5 or 6 extends between each of the three opposed pairs of vertexes of each octahedron. This description of my construction may now be summarized more simply as a truss structure comprising tension elements defining octahedra arranged face to face, and compression elements arranged along the three axes of each octahedron. The seemingly complex but truly simple forms of the octahedral units will be further understood by identifying the faces of the octahedra, the tension elements and the compression elements as follows: Eight faces of the octahedra: Three compression elements: From the foregoing tabulation of the truss elements, the student of this disclosure will appreciate the preponderance in tension elements over compression elements and the significant improvement thus obtained in the direction of increased utilization of the high tensile properties of the improved materials and alloys available today. The problem heretofore has not been the availability of materials of good tensile properties, but rather the ques tion of how such properties could be utilized more fully in the realm of building architecture; and how this could be done in a practical manner which would provide surfaces which could conveniently be cladded-eveu though such surfaces seem to be made up of a maze of wires and to be inherently spikey. How this can be done is now further disclosed with more particular reference to FIGS. 2, 4, 8 and 9 of the drawings: If we take a truss section of the extent comprised of six associated octahedra, it will be noticed that one face (1-2-3) of each of the six octahedra lies in a common surface. These faces of the six octahedral units are joined together vertex to vertex, and together encircle a hexagonal area. The six triangular faces 123 are enclosed by triangular capping members 8 which may be secured in any convenient manner as by bolting them to fittings 1, 2 and 3, FIG. 5, which may be apertured as at 9, FIG. 3, to receive bolts passin through aligned apertures 10 in overlapping corner portions of the triangular capping members. By this means, the capping members are secured to each other and to the underlying truss. In the preferred construction shown, the triangular capping members 8 are formed as panels having upwardly extending marginal flanges 11, FIG. 9. The hexagonal area within the circle of triangular panels 8, FIG. 2, may then be enclosed in any suitable manner. This may be done most advantageously with the use of a hexagonal capping member 12, FIG. 8, having downwardly extending marginal flanges 16 which fit over the upwardly extending flanges 11 at the edges of the hexagonal area. The hexagonal capping member 12 is advantageously formed with three adjoining diamond-shaped surfaces 13, 14, and 15 of hyperbolic-paraboloid form. Various materials may be employed in the cladding of the structure including formed or molded sheets of steel, aluminum, plastics, fiberglass or other suitable materials. In the representative construction shown, the triangular capping members 8 are made of steel and the six-sided capping members 12 are made of fiberglass-reinforced polyester resin. In the construction shown in FIG. 8,- this capping member is further reinforced along the ridges formed by the adjoining edges of the hyperbolic-paraboloids by hollow molded ribs 17 filled with a urethane foam 18. (The cladding construction which I have described forms an effective watershed by reason of the interlocking flanges of the several cladding members and the arrangement by which the water can flow from one triangular panel to another. These panels together form a maze of gutters which will serve to clear a heavy flow of rainwater.) In FIG. 6, I have illustrated a modified form of the fundamental octahedral unit in which the compression members extending between each of the three opposed pairs of vertexes 1-1, 22' and 3-3 of the octahedron are each made in two parts joined together centrally of the unit by a hub member 7 provided with three pairs of fittings aligned with the respective axes of the compression members. It will be observed that in the embodiment shown in FIG. 5, the compression members 4, 5 and 6 are arranged to bypass one another in the manner of the poles of a tepee. At the point of bypass, the members may be spaced from one another or be in contact. They may or may not be secured to one another at the point of bypass as desired. In the embodiment of FIG. 6, the compression members can be arranged so that their axes intersect, the single members 4, 5 and 6 here being replaced by the compound compression members ill-4b, 5a5b, 6a6b, respectively. When my invention is utilized in geodesic dome construction, some of the octahedral units will be arranged so that their triangular capping members encircle a pentagonal area as distinguished from the hexagonal area described with reference to FIGS. 2 and 3. This occurs at each vertex of the icosahedron, dodecahedron or tricontahedron on which the design of the geodesic dome is based. This aspect of geodesic construction is well known to architects familiar with such construction, and will be understood from the disclosure of my fundamental geodesic building construction Patent No. 2,682,235 where the pentagonal areas can be seen clearly in FIGS. 1 and 2. Thus in a geodesic dome constructed in accordance with my present invention, some of the octahedral units are arranged so that one face of each of six associated units lies in a common spherical surface, such faces of the six associated units being joined together vertex to vertex and enclosed by triangular capping members which encircle a hexagonal area in the common spherical surface, such hexagonal area being enclosed by a six-sided capping member adjoining each of the six triangular capping members; whereas, others of the octahedral units are arranged so that their triangular capping members encircle a pentagonal area in the commonspherical surface, such pentagonal area being enclosed by a five-sided capping member adjoining each of the five triangular capping members. This will be further understood from the diagram of FIG. 10. The area covered by this diagram can be compared with the ,area at the zenith Z of my geodesic patent aforesaid. Triangular capping members T, T1, T2, T3, H4, T5 encircle a hexagonal area which is enclosed by a six-sided capping member H which might, for example, be of the construction which has been described with reference to FIG. 8. Triangular capping members T, T1, T6, T7, T8 encircle a pentagonal area enclosed by a five-sided capping member P. Capping member P may be of simple pyramidal form ,as distinguished from the hyperbolic-paraboloid form of FIG. 8, or H in the diagram. Further, the form of the six-sided capping members may be modified according to the wishes of the architect; for example, they may be of the simple pyramidal form shown at H1 in the diagram. FIG. 11 illustrates a further development of the construction of FIG. 4, in which the proportions of the octahedral units are altered to create a flat floor or roof truss. This truss is then built up into two or more thicknesses (two as shown) in which every other truss is inverted. Here the smaller faces 1-2-3 of the two trusses are joined congruently. Similarly, two trusses may be joined in a manner which brings the larger faces 123' into congruent relation. FIG. 12 illustrates the application of my invention to a mast or tower structure. In this case the opposed faces 123 and 1'2'3 of the octahedrons are of the same size, and parallel to one another. FIG. 13 illustrates a modification of the FIG. 12 structure in which opposed faces 1-23 and 1' 3' are of different size, and are not parallel to one another. FIG. 14 illustrates an application of my invention to an asymmetrical structure which reveals the comprehensive adaptability of my invention to structures of irregular form. The octahedrons A, B, C, D, etc., can be varied in their relative proportions and shapes, grouped and extended as desired, while availing of the favorable weightstrength ratio obtained by reason of the preponderance of tension elements over compression elements. FIG. 15 illustrates a further modification of the octahedral units in which the twelve edges of each octahedron are in the form of structural shapes such as the angle irons of steel or aluminum shown at 19. Vertex members 1a, 2a and 3a correspond to members 1, 2 and 3 of FIGS. 5, 6 and 7. These are advantageously made as metal castings to which the structural shapes 19 are welded as 20. The construction thus comprises a plurality of interconnected units each of which comprises twelve members interconnected to form the edges of a self-supporting unit having eight triangular faces, the units being connected face to face so that each pair of adjacent units have one face and three members thereof in congruity. The faces which are connected in congruity are those which are shown spaced slightly apart, these faces being designed to be bolted together in the manner indicated by the exploded bolting elements, which pass through aligned apertures in the congruent edge members. In each of the embodiments described, my structure comprises a plurality of interconnected units each of which includes twelve members interconnected to form the edges of a figure having eight triangular faces, an outer face of the several units lying in a common surface and an inner face of the several units lying in a second common surface spaced from and parallel to the first. For example, in the embodiment of FIGS. 1-5 and 7, and with particular reference to FIG. 5, we have an outer face 1-2-3 and an inner face 1'23', these two faces lying in surfaces which are spaced from and parallel to one another. Notice that the outer face 1-2-3 is approximately one-half the size of the inner face 1'2'-3 and that the two faces are so oriented relative to one another that the vertices of the outer face lie substantially above the midpoints of the sides of the inner face. Above is used here in the sense of beyond or outside of; and it will be understood that if the truss extends in a generally horizontal direction, vertex 2, for example, of the outer face 12-3 will lie above the side 1'2'3' of the inner face 12-3', whereas, if the truss is located so as to extend in a generally vertical direction, vertex 2 will be beyond or outside of side 13'. If the inner and outer surfaces of the truss are parallel fiat planes arranged horizontally, vertex 2 will be directly above side 1-3. Again, if the common surfaces are concentric spherical surfaces, ver tex 2 will be disposed radially outside of the midpoint of side 1'3'. So in all cases it can be considered that the orientation of the outer and inner faces of each unit is such that the vertices 1, 2, and 3 of the outer face lie substantially above the midpoints of the sides of the inner face 1'2'-3'. The relative size and orientation of the inner and outer faces of each unit as described in the preceding paragraph makes it possible to interconnect the several units in a manner which joins the outer faces together vertex to vertex and which joins the inner faces together edge to edge. If the truss is inverted or turned inside out, the inner faces will be joined together vertex to vertex and the outer faces edge to edge. The terms and expressions which I have employed are used in a descriptive and not a limiting sense, and I have no intention of excluding equivalents of the invention described and claimed. I claim: 1. A truss structure comprising a network of tension members and compression members; the tension members being joined in three opposed pairs of junctions, the junctions of the tension members forming vertices lying in planes defining an octahedron, said tension members of adjacent octahedra being connected, with the connections therebetween defining a common plane of said adjacent octahedra, and said compression members extending between each of said three opposed pairs of junctions of said tension members of each octahedron. 2. A truss structure comprising a network of tension members and compression members; the tension members being joined in a multiplicity of three opposed pairs of junctions, the junctions of the respective tension members forming three opposed pairs of vertices lying at the vertices of eight triangular faces defining an octahedron, said tension members of adjacent octahedra being connected, the adjacent octahedra being positioned with a triangular face of one in face to face relationship with a triangular face of another, the connections between adjacent octahedra defining a first and a second common surface, one of the triangular faces of each octahedron lying in said first common surface and another of the triangular faces of each octahedron lying in said second common surface, and three of said compression members being positioned in criss-crossed relationship and extending between each of said three opposed pairs of junctions of each octahedron. 3. A truss structure for a geodesic dome comprising a plurality of interconnected self-supporting units each of which comprises twelve members interconnected at six junctions forming vertices of the respective units and with said twelve members forming the edges of the respective units, each unit having eight triangular faces, said units being connected face to face so that each pair of adjacent units have one face and three members thereof in congruity. 4. A truss structure in accordance with claim 3 in which one face of each of six associated units lies in a common spherical surface, said faces of said six associated units being joined together vertex to vertex and each being closed by respective ones of six triangular capping members which encircle a hexagonal area in said common spherical surface, said hexagonal area being enclosed by a six-sided capping member adjoining each of the six t-riangular capping members. 5. A truss structure in accordance with claim 3 in which one face of each of six associated units liesin a common spherical surface, said faces of said six associated units being joined together vertex to vertex and each being closed by respective ones of six triangular capping members which encircle a hexagonal area in said common spherical surface, said hexagonal area being enclosed by a six-sided capping member adjoining each of the six triangular capping members, said six-sided capping member being formed with three adjoining diamond-shaped surfaces of hyperbolic-paraboloid form. 6. A truss structure in accordance with claim 4 in which one face of each of five other associated units lies in said common spherical surface, said faces of said five associated units being joined together vertex to vertex and being closed by respective ones of five triangular capping members which encircle a pentagonal area in said common spherical surface, said pentagonal area being enclosed by a five-sided capping member adjoining each of the five triangular capping members. 7. A truss structure comprising a plurality of interconnected units each of which includes twelve members interconnected at six junctions forming six vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each having eight triangular faces including an outer face and an inner face, the outer face of the respective units lying in a common surface and the inner face of'the respective units lying in a second common surface spaced from and parallel to the first, said outer faces being approximately one-half the size of said inner faces and the outer and inner faces of each unit being so oriented relative to one another that the vertices of the outer face lie substantially above the mid-points of the edges of the inner face, the respective units being interconnected in a manner which joins the outer faces together vertex to vertex and the inner faces edge to edge. 8. A truss structure according to claim 7 in which said first and second common surfaces are parallel flat planes. 9. A truss structure according to claim 7 in which said first and second common surfaces are parallel curved surfaces. 10. A truss structure according to claim 7 in which said first and second common surfaces are concentric spherical surfaces. 11. A truss structure comprising a plurality of interconnected units each of which includes twelve members interconnected at six junctions forming six vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each having eight triangular faces including a first face and a second face, the first face of the respective units lying in a common surface and the second face of the respective units lying in a second common surface spaced from and parallel to the first common surface, one of said first and second faces of each unit being approximately one-half the size of the other of said first and second faces, and said first and second faces of each unit being so oriented relative to one another that the vertices of one such face lie substantially opposite the midpoints of the edges of the other such face, the respective units being interconnected in a manner which joins one of said first and second faces of the respective units together vertex to vertex and which joins the other of said first and second faces of the respective units together edge to edge. 12. A truss structure comprising a plurality of interconnected units each of which includes twelve members joined at six junctions forming three opposed pairs of vertices of the respective units and with said twelve members of the respective units forming the edges thereof, the respective units each being an octahedral figure having eight triangular faces including a first such triangular face and a second such triangular face, the first such face of the respective units lying in a common surface and the second such face of the respective units lying in a second common surface spaced from and parallel to the first common surface, said twelve members of the respective interconnected units being constituted by fiexible members capable of being stressed only in pure tension and each of said units further including three criss-crossed stiff members capable of being loaded as compression columns, said stiff members extending between each of the three opposed pairs of vertices of the octahedral figure formed by said eight triangular faces. References Cited UNITED STATES PATENTS 2,918,992 12/1959 Gelsavage 52-81 3,058,550 10/1962 Richter 52582 X 3,169,611 2/1965 Snelson 52578 X 3,220,152 11/1965 Sturm 52-81 X FOREIGN PATENTS 1,377,290 9/ 1964 France. 1,377,291 9/1964 France. FRANK L. ABBOTT, Primary Examiner. C. G. MUELLER, Assistant Examiner.

Description July 7, 1964 R. B. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 Sheets-Sheet l t 'z n ;:t IN VEN TOR. RICHARD BUCKMINSTER FULLER AT KY5. y 7, 1954 R. a. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 Sheets-Sheet 2 IN V EN TOR. RICHARD BUCKMINSTER FULLER ATT NEYS. July 7, 1964 FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24. 1961 8 Sheets-Sheet 3 IN V EN TOR. RICHARD BUCKMINSTER FULLER y 7, 1954 R. B. FULLER 3,139,957 SUSPENSION BUILDING Filed Jan. 24, 1961 8 sheets-Sheet 5 E uvvqvfie'. m5 RICHARD BUCKMINSTER FULLER July 7, 1 4 R. B. FULLER susvmsrou BUILDING 8 Sheets-Sheet 6 Filed Jan. 24, 1961 INVENTOR. RICHARD BUCKMINSTER FILLER AT 0mm. July 7, 1964 R. B. FULLER 3,139,957 SUSPENSION BUILDING Hulk nai N VEN TOR. ATTORNEYS. RIWARD BUCKMINSTER FULL R United States Patent 3,139,957 SUSPENSION BUILDING Richard Buckminster Fuller, 407 S. Forest St., Carbondale, Ill. Filed Ian. 24, 1961, Ser. No. 88,245 11 Claims. (Cl. 189-1) My invention relates to building construction. Summary 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. My new structure comprises a series of box frames of polygonal, cylindrical or other form, these frames being of progressively varying sizes arranged in a concentric array at sequentially different heights above a common plane of reference and in vertically overlapping spaced relation to one another. Tension elements such as flexible cables or wires extend between and are secured to adjacent pairs of the box frames in the series. These tension elements include tension members extending downwardly from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair. In this manner, successive frames of the series are suspended one from another in either a rising, descending or level series as may be desired. Other tension members extend upwardly from their points of securement to one frame of a pair of their respective points of securement to the other frame of a pair whereby successive frames in the series are anchored down one to another. The suspension members and anchor members complement one another in performing a third function, the provision of a tensioned buttress against tilting of the compression members comprised in the frames. Thus are satisfied the three functions of 1) suspension, (2) anchoring and (3) buttressing, all by the simplest arrangement of tension wires in combination with the series of frames as disclosed. Additionally, these tension wires act to stabilize the frames themselves, and furnish a tension system efficiently disposed for resisting torquing and counter-torquing of the frames about the central axis of the structure. These can be catalogued as functions (4) and (5). Still other tension members may be provided that will be disposed in radial planes containing the central axis of the structure. In the case of a structure utilizing a series of frames of polygonal form, the several tension members are secured to the vertexes of the polygons. Those tension members lying in radial planes will apply tension forces to the upper peripheries of the frames and thereby reduce compressive forces imposed on such peripheries by others of the tension mem bers. Description With reference to the drawings I shall now describe the best mode contemplated by me for carrying out my invention. FIG. 1 is an elevational view partly in vertical section illustrating the application of my invention to a roofed stadium or concert hall. 3,139,957 Patented July 7, 1964 ice FIG. 2 is a plan view of the FIG. 1 structure with the right-hand portion of the roof covering removed to reveal the suspension frame construction, taken as indicated at 2-2 in FIG. 1. FIG. 3 is an elevational view illustrating another embodiment of the invention, the right-hand portion being shown in diagrammatic vertical section. FIG. 4 is a similar view of another embodiment. FIG. 5 is a plan view of the suspension frame system of the FIG. 4 structure, taken as indicated at 5-5 in FIG. 4. FIG. 6 is a diagrammatic vertical section of a still further embodiment of the invention. FIG. 7 is a plan view of the FIG. 6 structure, roof covering omitted, taken as indicated at 7--7 in FIG. 6. FIGS. 8 to 17 inclusive are diagrammatic representations illustrative of the general scope of applicability of my suspension building system to various building forms with the use of different kinds of box structures and with several alternative dispositions of the suspension and anchoring cables, FIG. 8 being a vertical sectional view illustrative of flanged cylindrical box sections, FIG. 8a a plan view illustrative of an asymmetrical form of my construction, FIG. 9 a vertical sectional view illustrative of flanged box sections of frusto-conical form, FIG. 10 illustrative of the use of similar box sections of inverted frusto-conical form, FIG. 11 a plan view illustrative of a special elongated form of box section, FIG. 12 an isometric perspective view of another form of framing and one alternative arrangement of the suspension and anchoring cables, FIG. 13 a diagram analyzing the vertical components of the reach of the cables of FIG. 12, FIG. 14 a partial view similar to FIG. 12 with an alternative disposition of the cables, FIG. 15 a diagram analyzing the vertical components of the reach of the cables of FIG. 14, FIG. 16 a view similar to FIG. 14 showing a still further disposition of the cables, and FIG. 17 a diagram analyzing the vertical components of the reach of the cables of FIG. 16. FIG. 18 is a perspective view illustrating the application of my invention to a spherical or hemispherical structure based on the spherical octahedron. FIG. 19 is a detail cross-sectional view taken on the line 1919 of FIG. 18. In FIGS. 1 and 2 we see a structure embodying my invention in one of its preferred forms as applied, for example, to a roofed sports arena or stadium. The structure comprises a series of polygonal box frames 1 to 10 inclusive, 2, 3 and 4. In this particular construction each frame is comprised of upper chord members 11 and lower chord members 12 forming the upper and lower peripheries of the respective frames, and vertical compression columns or struts 13 extending between the vertexes of the polygon formed by the upper chord members 11 and the corresponding vertexes of the polygon formed by the lower chord members 12. Considering an individual frame as a whole, such frame is an annular form faceted into rectangles around its rim or periphery by the members 11, 12 and 13. The series of box frames 1 to 10 inclusive, 2, 3 and 4, are of progressively varying sizes and they are arranged in a concentric array at sequentially different heights above a common plane of reference (for instance, the horizontal plane of the foundation) and in vertically overlapping spaced relation one to another. Tension elements extend between and are secured to adjacent pairs of the box frames in the series, these tension elements including tension members 3 14, 14' which extend downwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are suspended one from another [function (1) of the Summary given at the beginning of this specification]. The tension elements also include other tension members 15, 15' extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another [function (2) of the Summary]. Tension members 14 and 15 may be arranged in crisscrossing pairs as shown in FIG. 2. In this particular embodiment the same tension members are crisscrossed whenviewed in plan, FIG. 2, as well as when viewed in elevation. The downwardly extending tension members may include members disposed in radial planes containing the central axis 16 of the structure, and the upwardly extending tension members 15 also may include members disposed in such radial planes. In FIG. 1 the particular tension members 14' and 15' which come into view are those which lie in one of such radial planes. In the preferred construction shown, the several tension members 14, 15, 14', 15 are secured to the respective polygonal box frames at the vertexes thereof. Also in this particular construction the domical structure formed by the series of suspended box frames is flattened on top by the provision of a series of box frames 10, 17 and 18 of progressively varying sizes arranged in a concentric array above the common horizontal plane of reference and in horizontally spaced relation one to another. As in the rest of the structure, we have the tension members 14, 14' functioning as suspension members, and 15, 15 functioning as anchoring members. All such tension members 14, 14', 15, 15' complement one another in performing a third function, the provision of a tensioned buttress against tilting of the compression members 13 comprised in the frames [function (3) of the preceding Summary]. Additionally, these tension members act to stabilize the frames themselves and furnish a tension system efiiciently disposed for resisting torquing and counter-torquing of the frames about the central axis 16 of the structure [functions (4) and (5) of the Summary]. Further, the tension members 14', 15' which extend outwardly from the upper and lower peripheries of the frames will apply tension forces which will reduce compressive forces imposed on such peripheries by others of the tension members. Annular frames 1 to 10 inclusive are illustrative of a rising series of frames, annular frames 1, 2, 3 and 4 illustrative of a descending series of frames, and annular frames 10, 17 and 18 illustrative of a level series. The level series may terminate in a single central strut or annulus 19. Beginning at the base of the structure we have the annular frame 4 from which is suspended at a higher elevation the frame 3 from which in turn is suspended the frame 2 and then in succession we have suspended each from the other in the order named the frames 1, 2, 3 and so on, altitude being gained meanwhile in the progressively stepped suspension system. Similarly, frame 17 is suspended from frame 10, frame 18 from 17, and center post 19 from frame 18. As in the suspension bridge the tension aspect of the structure is highly significant through utilization of the more favorable tensile strengths of materials as contrasted with their vastly inferior compressive strengths. It would be difficult to imagine an upside down suspension bridge and yet that is in effect what I have achieved when my structure is considered in any given vertical profile. Altitude is gained by breaking up the suspension systeminto steps and stability of the stepping is attained by the three dimensional aspect of the structure as contrasted with the essentially two dimensional system of the suspension bridge. The end result is a tremendous saving through the realization of a larger building per unit weight of the material employed in its construction, this in turn being the benefit conferred by my discovery of how to get more use from the most favorable property of materials, namely tensile strength. Essentially I have devised a building construction which in large measure replaces heavy columns and beams with a light spidery array of tension wires or cables. The structure can be roofed in many ways. In the embodiment of FIGS. 1 and 2, roofing sheets 20 of trapezoidal form are shown. The method by which these are attached and the detail of their construction are not an essential part of my present invention. In FIG. 3 I have shown a modified frame construction in which the compression members 21, 22, etc. are comprised of elliptical struts designed for increased efficiency in the use of materials in compression. Pagoda roofing is here employed to advantage as an eificient watershed with provision for good ventilation by means of windows or louvres 54 set well under the overhangs in the roof. In FIGS. 4 and 5 the polygonal frames comprise a series of diamond shaped frames 24 to 27 inclusive. Suspension wires 28, 28' suspend each successively higher frame from the lower-numbered frame of the series. Anchoring wires 29, 29 disposed in radial planes containing the central axis of the structure are provided as before. Both the wires 28, 28' and the wires 29, 29' are secured to the upper edge of the lower frame of each pair of frames, in this respect representing a variation from the crisscrossing arrangment of FIGS. 1 and 2. The roof structure here simplifies into a generally pyramidal form. It is essential to understand that the box or annular frames of my invention may be either skeletal as when made of strust or tubes as I have described, or continuous as when made in the form of sheets, plates or panels. In FIG. 8 we see an example of the latter construction in which the frames or annuli are comprised of simple cylinders 30, 31 and 32. These may have marginal flanges 33 as shown. In the embodiment typified here the suspension wires 34 extend downwardly from the upper edge of the lower frame of a pair to the lower edge of the upper frame of the pair, and the anchor cables 35 extend from the lower edge of the lower frame of a pair to the lower edge of the upper frame of the pair (instead of to the upper edge of the pair as in the embodiment of FIGS. 1 and 2). The system of wires 35 may be projected as at 36 if desired, providing a continuous line of tension from the top to the base of the structure. FIG. 8a shows the application of my invention to an asymmetrical structure comprising the frames 37, 38, 39, 53, which may be of any desired peripheral contour. FIG. 9 represents another kind of continuous annular frame 40, 41, 42, being one of frusto-conical form. In FIG. 10 the frusto- conical frames 43, 44, 45 are inverted from the position of those in FIG. 9. If the sheet containing FIGS. 8, 9 and 10 is inverted, we see three additional variants in which either cylindrical or frusto-conical frames are arranged in what I have previously referred to herein as a descending series. This would equate to the series 2, 3, 4 in FIG. 1. FIG. 11 shows the application of my invention to an elongated structure of involute-evolute form comprising end sections 46, 47, of generally hexagonal pyramidal form and a connecting section of involute-evolute form, affording added strength to such an elongated structure. The disposition of the suspending-anchoring-buttressing cables may be generally similar to that in the structures already described. The construction of the frames themselves as seen in elevation will be generally similar to that described with reference to FIG. 1. FIGS. 6 and 7 shows the application of my invention to a structure of hexagonal form comprising the series of hexagonal frames 49, 50, 51, 52, each higher-numbered frame being suspended from the lower-numbered frame of the series. Here the extent of vertical overlapping between successive frames varies whereas the horizontal spacing remains contsant. This is incontradistinction to the arrangement of FIG. 1 in which the horizontal spacing between successive frames varies. The feasibility of varying both vertical overlap and horizontal spacing lends great flexibility to the design of the structure. FIG. 12 shows the application of my invention to a rectangular form of structure comprising the series of rectangular frames 55, 56, 57. As before, these frames can be considered to be made up of struts in an open or skeletal framework or to be continuous as when made in the form of sheets or panels. The frames themselves may if desired be triangulated through the use of diagonal wires extending between the diagonally opposite corners of each side or facet of the frame. FIG. 13 may be considered as a diagrammatic section taken either on the central diagonal plane or a central plane bisecting the sides of the frames, s being the suspension members and a the anchoring members. Regarding FIG. 13 as the diagonal section, s and a are both disposed in a vertical plane containing the axis of the structure. Regarding FIG. 13 as the section bisecting the sides of the frames, s and a are crisscrossed both horizontally and vertically as will be understood from FIG. 12. In either case FIG. 13 gives a picture of the vertical components of the reach of the cables. FIGS. 12-13, FIGS. 14-15 and FIGS. 16-17 are comparative views illustrative of the general scope of applicability of my suspension building system to structures utilizing several alternative dispositions of the suspension and anchoring cables. FIGS. 14 and 16 represent portions of the same frame arrangement shown in FIG. 12 but the arrangement of the tension members is different. The difference in this arrangement may best be discerned in FIG. 15 as compared with FIG. 13. In FIG. 15 suspension cables .9 extend in the same manner as the cables s of FIG. 13 but the anchoring cables a extend between the upper corners of the successive frames in the series. FIGS. 16 and 17 shows another alternative arrangement of the tension members in which the anchoring cables a" extend between the lower comers of the successive frames in the series. Thus in the construction of FIGS. 12-13 we have vertically crisscross cables whereas in FIGS. 14-15 and FIGS. 16-17, these cables do not cross one another although the tensioning pattern in all cases is triangulated, resulting in an omni-triangulated building construction. The differing patterns of triangulation may be combined in various ways, using one system at one side or facet of the structure and an alternate system in the adjacent side as may be desired. Another alternative arrangement would be to use only suspension elements s, s or s" at one side of the series of frames and only anchoring elements a, a or a" in the side adjacent and continuing this alternating suspension and anchoring in succeeding sides. FIGS. 18 and 19 show the application of my invention to a spherical structure or to a segment of a spherical structure based on the spherical octahedron. Here we have a hemispherical dome comprising four spherical triangles of the octahedron defined by the intersections of three great circles 58, 59, 60. Relating these to the globe we have the great circle 58 at the equator, 59 at 0 and 180 longitude, and 60 at 90 and 270 of longitude. Two of the spherical triangles of the octahedron appear at 61 and 62. Each is subdivided by means of any selected number of spherical triangles of progressively smaller sizes arranged in a concentric array. These several concentric triangles form the inner or outer edges of frames of either skeletal or continuous form. Considering the frame array for spherical face 61 of the octahedron, we have the frames 63, 64, 65, 66. Considering the several frames of the series to be of the same radial depth (67=68=69=70), and reorienting the structure so that a line containing the center of spherical face 61 and the center of the sphere is vertical, we have, as in other forms of my invention, a series of box frames of progressively varying sizes arranged in a concentric array at sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another. Also, as before, tension elements 71, 72, FIG. 19, extend between and are secured to adjacent pairs of the frames in the series. Tension elements 71 extend downwardly, i.e. inwardly of the sphere, from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair whereby successive frames in the series are suspended one from another. Tension members 72 extend upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down, i.e. inwardly of the sphere, one to another. It will be understood that the several tension elements serve all of the five functions described hereinabove, namely those of suspension, anchoring, buttressing, stabilizing of the frames themselves and resisting torquing and countertorquing of the frames about a line passing through the centers of the sphere and of the octahedral face. It may be mentioned that in FIG. 18 I have for simplicity of illustration omitted tension elements 71 and 72, the general arrangement of which will be understood from the description of the other forms of my invention. Also, it will be understood that any of the described alternate arrangements of the tension elements may be employed as desired. The terms and expressions which I have employed are used in a descriptive and not a limiting sense, and I have no intention of excluding such equivalents of the invention described as fall within the scope of the claims. I claim: 1. A structure comprising a series of box frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair of their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 2. A structure according to claim 1 in which said tension elements also include other tension members extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another. 3. A structure comprising a series of cylindrical frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the cylindrical frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby succesive frames in the series are permanently suspended one from another in predetermined fixed positions. 4. A structure comprising a series of polygonal box frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the polygonal box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 5. A structure according to claim 4 in which said tension elements also include other tension members extending upwardly from their points of securement to the lower frame of a pair to their respective points of securement to the upper frame of the pair whereby successive frames in the series are anchored down one to another. 6. A structure according to claim 4 in which said downwardly extending tension members include members disposed in radial planes containing the central axis of the structure. 7. A structure according to claim 6 in which said downwardly extending tension members are secured to tle respective polygonal box frames at the vertices there- 8. A structure comprising a series of frusto-conical frames of progressively varying sizes arranged in a concentric array at predetermined sequentially different heights above a common plane of reference and in vertically overlapping spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the frusto-conical frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to the lower frame of a pair to their respective points of fixed securement to the upper frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 9. A structure comprising a series of box frames of progressively varying sizes arranged in a concentric array above a common horizontal plane of reference and in horizontally spaced relation one to another, and tension elements extending between and fixedly secured to adjacent pairs of the box frames in said series, said tension elements including tension members extending downwardly from their points of fixed securement to one frame of a pair to their respective points of fixed securement to the other frame of the pair whereby successive frames in the series are permanently suspended one from another in predetermined fixed positions. 10. A structure according to claim 9 in which said tension elements also include other tension members extending upwardly from their points of securement to one frame of a pair to their respective points of securement to the other frame of the pair whereby successive frames in the series are anchored down one to another. 11. A structure according to claim 10 in which said downwardly extending tension members include members disposed in radial planes containing the central axis of the structure. References Cited in the file of this patent UNITED STATES PATENTS 2,576,389 Craighead etal Nov. 27, 1951 2,621,765 Wood Dec. 16, 1952 2,689,025 Yates Sept. 14, 1954 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 139.957 July 7, 1964 Richard Buckminster Fuller It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patentshould read as corrected below. I Column 1, line 41, for "of", second occurrence. read e Signed and sealed this 10th day of November 1964. (SEAL) Attest: ERNEST W. SWIDER Allcsting Officer EDWARD J. BRENNER Commissioner of Patents

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