R. B. FULLER
BUILDING CONSTRUCTION
6 Sheets—Sheet 1
INVENTOR
RICHARD BUCKMI NSTER FULLER ;' BY
June 29 1954 R. B. FULLER
BUILDING CONSTRUCTION
Filed Dec. 12 1951 6 Sheets—Sheet 2
21
ATTORNEY
INVENTOR.
RICHARD BVCKMINSTER FULLER Y
Jame 29 1954 R. B. FULLER
        BUILDING CONSTRUCTION
Filed Dec. 12 1951 6 Sheets—Sheet 3

INVENTOR. if/CHARD BUCP(IIINSTER FULLER
hull
.June 29 1954
Filed Dec. 12 1951
R. B. FULLER
BUILDING CONSTRUCTION

INVENTOR.
RICHARD BUCKMINSTER FULLER BY
June 29 1954 R. B. FULLER
BUILDING CONSTRUCTION
Filed Dec. 12 1951 6 Sheets—Sheet 5
48 .S7 18 19 54 48
Jso
INVENTOR. RICHARD BUCKMINSTER FULLER
BY
ATTORNEY
June 29 1954 R. B. FULLER
        BUILDING CONSTRUCTION
Filed Dec. 12 1951 6 Sheets—Sheet 6
62
INVENTOR. RICHARD BUCKMI NSTER FULLER
BY ATTORNEY
60
61
61
Patented June 29 1954
UNITED STATES PATENT OFFICE

BUILDING CONSTRUCTION
Richard Buckminster Fuller Forest Hills N. Y.
Application December 12 1951 Serial No. 261 168
13 Claims. (Cl. 108—1)
5 10 15
25
30 35 40 45 50 55
1
My invention relates to a framework for en-closing space.
SUMMARY
A good index to the performance of any building frame is the structural weight required to shelter a square foot of floor from the weather. In conventional wall and roof designs the figure is often 50 lbs. to the sq. ft. I have discovered how to do the job at around 0.78 lb. per sq. ft. by constructing a frame of generally spherical form in which the main structural elements are interconnected in a geodesic pattern of approximate great circle arcs intersecting to form a three-way grid and covering or lining this frame with a skin of plastic material.
My "three-way grid" of structural members results in substantially uniform stressing of all members and the framework itself acts almost as a membrane in absorbing and distributing loads. The resultant structure is a spidery framework of many light pieces such as aluminum rods tubes sheets or extruded sections which so complement one another in the particular pattern of the finished assembly as to give an extremely favorable weight-strength ratio and withstand high stresses. For example the "8C270 Weather-break" constructed in accordance with my invention will support 7 lbs. with each ounce of structure and is able to withstand wind velocities up to 150 miles per hour. It is a dome 49 ft. in diameter enclosing 20 815 cu. ft. of space yet the frame is made of light short struts which pack into a bundle 2 ft. by 4 ft. by 5 ft. weighing only 1000 lbs. The plastic skin weighs 140 lbs. making the total weight of this "weatherbreak" a mere 1140 lbs.
Definitions of terms
The basic and fundamental character of the inventive concept herein disclosed makes it desirable to define carefully certain terms some of which are used with special connotation as follows:
Geodesic.—Of or pertaining to great circles of a sphere or of arcs of such circles; as a geodesic line hence a line which is a great circle or arc thereof; and as a geodesic pattern hence a pat-tern created by the intersections of great circle lines or arcs or their chords.
Spherical.—Having the form of a sphere; includes bodies having the form of a portion of a sphere; also includes polygonal bodies whose sides are so numerous that they appear to be substantially spherical.
Icosahedron.—A polyhedron of twenty faces.2
Spherical icosahedron.—An icosahedron "exploded" onto the surface of a sphere; bears the same relation to an icosahedron as a spherical triangle bears to a plane triangle; the sides of the faces of the spherical icosahedron are all geodesic lines.
Icosacap.—Five spherical triangles of a spherical icosahedron having a common vertex.
Grid.—A pattern of intersecting members lines or axes; usually intersecting great circles forming patterns made up of equilateral triangles diamonds or hexagons.
Equilateral.—Having all the sides approximately equal. The extent of variation in length of sides is determined trigonometrically or empirically by constructing three-way grids on the modularly-divided edges of the faces of a spherical icosahedron.
Modularly divided.—Divided into modules or 20 units of substantially equal length.
Framework.—The frame of a structure for en-closing space; may be skeletal as when made of interconnected struts; or continuous as when made of interlocking or interconnected sheets or plates.
The meanings of these and other terms used in describing the invention will be more fully comprehended when considered with reference to the accompanying drawings and diagrams and the explanation thereof.
In its general arrangement my building framework is one of generally spherical form in which the longitudinal centerlines of the main structural elements lie substantially in great circle planes whose intersections with a common sphere form grids comprising substantially equilateral spherical triangles. The visible pattern formed by the structural elements themselves does not necessarily show grids of equilateral triangles for the visible grids may be equilateral triangles equilateral diamonds or equilateral hexagons the diamonds being made up of two equilateral triangles and the hexagons being made up of six equilateral triangles. The individual triangles diamonds or hexagons as the case may be may be made of straight or flat elements in which circumstance they define flat or plane figures; or they may be made of arcuate or spherical form to define spherical figures. Either way the complete structure will be spherical or substantially so. And either way the individual structural elements are so arranged as to be aligned with great circles of a common sphere.
In my preferred construction the grids are formed on the faces of a spherical icosahedron.

3
Each of the twenty equal spherical equilateral triangles which form the "faces" of this construction is modularly divided along its edges. Lines connecting these modularly divided edges in a three-way great circle grid provide the out-line for the plan of construction. I have found that if the structural members be aligned with the lines of the grids the resulting framework will be characterized by more uniform stressing of the individual members than is possible with any construction heretofore known. The structural members may be aligned with all lines of the three-way grid or just with selected ones of those lines. If the members are arcuate or spherical they will coincide with the grid lines; if they are straight or flat they will be chords of the great circles which are the grid lines.
A further general aspect of my preferred construction which may be noted here is that there is a "six-ness" throughout the pattern of structural elements on each face of the spherical icosahedron except that at each vertex where five faces join at the center of an icosacap there is a "rave-ness." In the case of a skeletal frame-work made up of struts in a pattern of equilateral triangles this "six-ness" is manifested by the fact that there are six such triangles around every vertex except at the vertexes of the icosacaps where the "five-ness" is manifested by the fact that there are only five such triangles around those vertexes. Similarly in the case of a continuous framework made up of diamond-shaped sheets we find a "five-ness" only at the vertexes of the icosacaps where five sheets toe in to the one point. This aspect of five-ness and six-ness will be described more in detail further on and need be mentioned only in general terms here so as to lay a foundation for the description of various specific frameworks built according to the invention.

DESCRIPTION
In the drawings:
Fig. 1 is an elevational view of a building framework constructed in accordance with my in vention and exemplifying a preferred form thereof; and Fig. 2 is a top plan view of the same framework. These views are necessarily some-what schematic because of the limitations imposed by the smallness of the scale to which they are drawn making it impossible to show the de-tail of individual struts or of the fastenings which hold them together.
Fig. 3 is a diagrammatic perspective view of an icosahedron; and Fig. 4 a view of the same icosahedron after it has been "exploded" onto the surface of a sphere. These views are included to explain the structural basis of the main out-lines of the framework of Figs. 1 and 2.
Fig. 5 is a detail plan view of a portion of the framework of Figs. 1 and 2 being that portion which immediately surrounds the top central vertex i. e. the central part of the icosacap seen in Fig. 2.
Fig. 6 is a vertical section on the line 6—6 of Fig. 5.
Figs. 7 and 8 are detail views of my preferred form of strut fastening. Fig. 7 is a central vertical cross-sectional view through the fastening with two struts fixed therein one of these being shown in central section and the other in elevation. Fig. 8 is a horizontal sectional view taken as indicated at 8—8 in Fig. 7 one of the struts being shown in elevation.4
Fig. 9 is a detail sectional view taken on the line 9—9 of Fig. 7.
Fig. 10 is a diagrammatic plan view of a modified construction in which the vertexes of
5 the pentagons and adjoining hexagons are offset inwardly to form an "involuted" truss-like structure. This view represents a portion of the framework similar to that shown in Fig. 5. How-ever instead of showing the framework itself
10 the planes of the equilateral triangles formed by the struts of the framework are shown as though they were triangular panels so as to permit shading of the view in such a way as to pictorialize the resulting "dimpled" surface.
15 Fig. 11 is a diagrammatic cross-sectional view taken on the line II—1I of Fig. 10.
Fig. 12 is a diagrammatic cross-sectional view similar to Fig. 11 showing a further modification in which the vertexes of the pentagons and ad-
20 joining hexagons are offset outwardly to form an "involuted" truss-like structure which is the inside-out of the structure of Fig. 11.
Fig. 13 is a fragmentary plan view of another embodiment of the invention and Fig. 14 is a
25 transverse sectional view of the same taken as indicated at 14—14 in Fig. 13. Figs. 13a and 13b are detail perspective views of certain component parts of the truss illustrated in Figs. 13 and 14.
Fig. 15 is a diagrammatic plan view illustrating
30 a portion of a framework in which the main structural elements consist of interconnected sheets.
Fig. 16 is a detail plan view of one of the sheets used in the framework of Fig. 15 and Fig. 17
35 is a detail longitudinal sectional view of such a sheet taken as indicated at 13—17 in Fig. 16.
Fig. 13 is a further detail view of the Fig. 15 framework showing the manner in which four adjacent sheets are interconnected or interlocked.
40 The framework construction illustrated in Figs. 1 to 9 inclusive is representative of the best mode devised by me of carrying out my invention particularly as utilized in structures up to approximately 50 feet in diameter. The struts which
45 comprise the structural elements of this frame-work form a portion of a spherical icosahedron 20 whose modularly divided edges 21 are inter-connected by three-way great circle grids 22. A spherical icosahedron has been defined above
5o as an icosahedron "exploded" onto the surface of a sphere. This definition will be further explained by reference to Figs. 3 and 4 Fig. 3 being a diagrammatic perspective view of an icosahedron and Fig. 4 a view of the same icosahedron
55 exploded or projected onto the surface of a sphere. The icosahedron has twenty equal equilateral triangular faces. The spherical icosahedron has twenty equal equilateral spherical triangular "faces." As used here the term "face" refers
60 to an imaginary spherical surface bounded by the sides or edges of one of the twenty spherical triangles.
The edges of each spherical triangle are modu-
larly divided and are interconnected by the
05 three-way great circle grids 22 previously men-
tioned. These grids are formed of a series of
struts each of which constitutes one side of one
of the substantially equilateral triangles defined
by the lines of the grid. Each strut 23 is aligned
70 with a great circle of the sperical icosahedron.
Otherwise stated the longitudinal centerline of
each strut or main structural element 23 lies
substantially in a great circle plane. In the
complete framework the longitudinal centerlines
75 of the main structural elements 23 lie substan-
2 882 235
5 10 15 20 25
45
60 65 70 75
5
tially in great circle planes whose intersections with a common sphere form grids 22 comprising substantially equilateral triangles.
The number of modules into which each edge of the spherical iscosahedron is divided is largely a matter of choice. In the framework of Figs. 1 2 5 and 6 the number is 16. Therefore we say the frequency is 16. But it might be 8 or 4 or some other number. Generally speaking the larger the structure the greater will be the frequency selected in order to keep the sizes of individual struts within practicable limits for ease of manufacture storage packing shipment handling and erection. I prefer to use light metal pieces for the struts e. g. aluminum tubes as shown in Figs. 7 and 8. One metal alloy presently considered most suitable is the aluminum alloy known generally under the designation 61ST. A tubular strut size found satisfactory for structures 40 ft. in diameter is approximately 4 ft. long by 17/3" outside diameter by 0.032" wall thickness. In general I prefer to use struts which have a ratio of 24 units in length to 1 unit in transverse dimension i. e. the "slenderness" ratio is 24 to 1. The frequency of the pattern as above defined can be selected with view to maintaining the optimum slenderness ratio for each size of framework.
The struts 23 may be interconnected by sliding joints locked by gravity compression acting throughout the great circle pattern of the frame-work as a whole. In erecting the framework it is best to start by assembling the struts which are to form the very top of the dome i. e. at the center of the icosacap seen in Fig. 2. This can be done on the ground. Working radially outward in all directions the dome will begin to take form and will gradually be lifted as the work proceeds until in the end its rest with its lowermost struts against the ground or on a suit-able foundation prepared to receive it. It may be locked to the foundation by great circle bands or cables preferably extending along the great circle lines which define the edges of the icosahedron. If a poured concrete foundation is used the lowermost struts and fastenings or the ends of such struts may be embedded in the foundation in which case the concrete or portions thereof is poured after erection of the frame-work has been completed. Alternatively the lowermost struts and/or the fastenings may be anchored to individual concrete foundation posts or to eye-bolts or other fastenings in such posts. In this arrangement any suitable auxiliary fastenings may be used to lock the framework to the foundation fastenings such as bolts cables turnbuckle rods etc. this being largely a matter of choice depending upon the type of construction best suited for a particular purpose.
Referring again particularly to Figs. 1 and 2 the ground line or foundation line is indicated at A—A in Fig. 1 and the components of the framework are so oriented that the midpoint of the pentagon at the center of an icosacap coincides with the zenith Z of the framework. In some cases however it may be preferred to shift the orientation of the framework as for example to an orientation which would result from using the line A'—A' as the ground or foundation line in which case the zenith Z' would no longer coincide with the midpoint of an icosacap but instead would coincide with a point within one of the spherical triangles which form the faces of the icosahedron. If the sheet of the drawing on which Fig. 1 appears be turned so that its right-hand longer edge becomes the bottom of the55 inner surface of inner part 27 of the fastener.
6
sheet that part of Fig. 1 which is bounded by Z'A'A' becomes the right-hand portion of the reoriented framework. Note that with this particular orientation the base line A'A' is a geodesic line completely defined by struts of the frame-work. This provides a convenient foundation line and one which lends itself well to anchoring of the framework to its foundation. In Figs. 1 and 2 however I have chosen the zenith Z orientation in order to provide a clear illustration in Fig. 2 of a complete icosacap as defined hereinabove.
One of the characteristics of the completed framework is that it is virtually self-locking. Once properly assembled in the manner described it will not come apart except by more or less uniform expansion of all its parts. However be-cause the framework is somewhat resilient localized forces acting outwardly against the inside of the structure may under certain conditions tend to expand one portion of the framework and produce what might be described as some-thing akin to a blowout in a pneumatic tire. To resist such forces and to assist in holding the struts together during erection it is best that the mean for fastening the ends of the struts be such as to lock them positively in place in this respect supplementing the self-locking action described above and giving added strength to 30 the framework by reason of the fixed-end con-
struction thus provided.
My preferred form of fastening is shown in
Figs. 7-9. It is a ball-like "fist" configuration
designated generally at 24 comprising comple-35 mentary parts 25 and 27. In the specific con-
struction illustrated 25 is the outer part and 27
the inner part. These parts are clamped to-
gether by means of a bolt 28 a coil spring 29
being provided to afford a certain amount of re-
40 siliency in the fastening which is particularly
useful during erection of the structure. As seen
in Fig. 7 outer part 25 is in the general form of
an inverted bell the edge of which is turned
back on itself to provide a curved flange 26 com-
plementary to the curved flange of inner part
27. Affixed to each end of each strut 23 is an
attaching member 30 having a tubular body por-
tion 45 the shouldered end 46 of which fits with-
in the end of the strut. Attaching member 30
50 may be secured to the strut 23 by means of a rivet
pin or bolt 31. Each fastening member has an
inwardly extending lug 32 and an outwardly ex-
tending lug 35. Lug 32 has a pair of flanges 34
with arcuate edges conforming to the arc of the

Similarly lug 35 has a pair of flanges 36 whose arcuate edges conform to the inner surface of flange 26 of outer part 25. A pair of flanges 33 at the end of fastening 30 have arcuate edges con-forming to the outer surface of the bell-like portion of outer fastening 25. The arrangement is such that the longitudinal centerline of struts meeting at any particular fastening 24 27 can be adjusted to different angles so that the struts will form chords of great circles of the framework as a whole. As the framework is erected it will tend to assume the general spherical form of the dome for which parts have been designed. Once it has assumed such form the individual fastenings are tightened compressing the coil springs 29 to the desired extent. If the fastenings are tightened to the extent which compresses springs 29 until they are driven solid maximum rigidity is obtained. However if greater flexibility is de-sired in the completed structure bolts 28 will

8
tagon at the midpoint of an icosacap i. e. an area corresponding to the central portion of Fig. 5 (except of course that this is a different type of framework than that shown in Fig. 5). The
5 framework is made up of struts similar to the struts 23 described with reference to the frame-work of Figs. 1 2 5 and 6 these struts being connected together by fastenings which may be similar to those described with reference to Figs. 7-9.
10 The framework may be considered as made up of a series of tripods one of which is shown in Fig. 13a consisting of three struts 47 joined at the center of the tripod by fastening 48. This particular tripod may be described as an out-
15 wardly pointing tripod. Its central vertex as represented by fastening 48 lies in the main or outer spherical surface 51 and its base lies in spherical surface 52 concentric with surface 51. Arranged in complementary fashion to the. out
20 wardly pointing tripods are inwardly pointing. tripods made up of three struts 49 joined together by fastening 50. Its central vertex as represented by fastening 50 lies in the inner spherical surface 52 and its base lies in the outer spherical
25 surface 51. Two such complementary tripods are shown in Fig. 13b. The. feet of the outwardly pointing tripods are joined together by tension members 53 which may be made of wires or cables. The feet of the inwardly pointing tripods are con-
J0 nected by similar tension members. 54.
In Figs 13 and 14 the struts 47 of all of the
outwardly pointing tripods have been shown with-
out any surface shading so that they appear light
in the drawing whereas the struts 49 of all the s inwardly pointing tripods have been shown with
surface shading so that they appear dark in
the drawing. Thus the "light" tripods are dis-
posed with their vertexes in spherical surface 51
and the "dark" are disposed with their vertexes 40 in spherical surface 52. Tension members 55 ex-tend diagonally between the respective feet of the light and dark tripods. These tension members as viewed in plan in Fig. 13 present a hexagonal outline alternate corners of which are connected by the aforesaid tension members 53 and 54 tension members 53 forming a triangle made up of chords of spherical surface 52 and tension members 54 forming a triangle made up of chords of spherical surface 51. The resultant basic pattern of the outer spherical icosahedron in surface 51 is the same as that illustrated in Fig. 5. The same is true with respect to the resultant basic pattern of the inner spherical icosahedron in surface 52. In effect therefore we have here two concentric spherical icosahedrons joined by diagonal struts and tension members. The framework is tightened into a final rigid structure by means of tension members 56 extending radially with respect to spherical surfaces 51 and 52 between the fastenings 48 and 50 at the apexes of the light and dark tripods respectively. If desired turnbuckles may be used in these tension members to secure the desired final tension to hold the structure with the proper degree of rigidity.
At the vertexes of the icosacap the framework assumes a pentagonal form as clearly shown at the center of Fig. 13. At such points in the structure we have an inwardly (or outwardly) pointing pentagonal strut arrangement in place of the two complementary tripods which characterize the rest of the framework where the pattern is. hexagonal. I prefer to bridge over the outer side or base of. the pentagonal strut arrangement at each vertex. In the specific framework. show;
7
be tightened to a lesser extent in which case the springs 29 will not be driven solid. Suitable lock nuts or lock washers may' be used to hold the parts in the desired final adjustment.
In Fig. 7 bolt 28. is provided with an eye 37 at its inner end which is useful in attaching the plastic skin inside of the framework. Bolt 28 passes through openings 38 39 in the outer and inner parts 25 21 respectively of fastening 24.
Reference is now made to the modified construction illustrated in Figs. 10 and 11. Fig. 10 represents a portion of the framework similar to that shown in Fig. 5. However instead of showing the framework itself the planes of the equilateral triangles formed by the struts of the framework are shown as though they were triangular planets (instead of spaces outlined by the struts). This has been done to permit use of shading in such a way as to pictorialize the "dimpled" surfaces of this particular framework. The "dimples" are formed by inwardly offsetting the vertexes of the pentagons 40 and adjoining hexagons 41 to form what I term an "involuted" truss-like structure. This places all the inwardly offset vertexes substantially in a spherical surface 42 concentric with the main spherical surface 43. The main spherical surface is defined by the ends of the struts of the bases of the pentagons 40 and hexagons 41. The resulting structure is like a spherical truss defining inner and outer substantially spherical surfaces of concentric spheres. This framework based on two spheres is somewhat stiffer and less resilient than the framework of Figs. 1 and 2 based on a single sphere and I consider the former best suited for the construction of domes in sizes ranging between approximately 50 and 140 feet in diameter. The struts which extend inwardly to the vertexes or points of the dimples are made somewhat longer than they would be in the single sphere construction so that upon assembly formation of the dimples is an inherent function of the lengths of the respective struts.
In the further modification illustrated by Fig. 12 the dimples are inverted. This framework and the framework of Figs. 10 and 11 can be made of the same kind of struts described with reference to Figs. 5 and 6 and can be put together with the same type of fastening described with reference to Figs. 7 and 8 although if desired other forms of struts and fastenings can be used with-in the limits of the appended claims. It will be observed that the fastenings of Figs. 7 and 8 allow for offsetting of the selected vertexes. (Note the clearance at 44.) Note also that in these modified constructions the struts which extend to the offset vertexes while no longer lying substantially in a spherical surface still are aligned with great circles of a common sphere; and such
struts still lie substantially in great circle planes whose intersections with a common sphere form grids comprising equilateral triangles. These inwardly extending struts also are chords of great circles of the framework.
Reference is now made to another embodiment of the invention as illustrated in Figs. 13. and 14. This is a variant of the frameworks of Figs. 10-12; like them it is based on two spheres. However the framework of Figs. 13 and 14 is more complex and comprises a truss formed of compres- 70 sion and tension members. I consider this type of framework best suited for the construction of domes in sizes from approximately 140 feet in diameter and upwards. Fig. 13 covers a small area of the framework. centering about the pen- 75