US20070163185A1 - Means and methods for construction and use of geodesic rhombic triacontahedron - Google Patents

Means and methods for construction and use of geodesic rhombic triacontahedron Download PDF

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US20070163185A1
US20070163185A1 US11/624,470 US62447007A US2007163185A1 US 20070163185 A1 US20070163185 A1 US 20070163185A1 US 62447007 A US62447007 A US 62447007A US 2007163185 A1 US2007163185 A1 US 2007163185A1
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dome
vertices
domes
icosahedron
geodesic
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Michael Morley
David Henderson
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Morley Michael T
Henderson David G
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    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B7/00Roofs; Roof construction with regard to insulation
    • E04B7/08Vaulted roofs
    • E04B7/10Shell structures, e.g. of hyperbolic-parabolic shape; Grid-like formations acting as shell structures; Folded structures
    • E04B7/102Shell structures
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32Arched structures; Vaulted structures; Folded structures
    • E04B1/3205Structures with a longitudinal horizontal axis, e.g. cylindrical or prismatic structures
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32Arched structures; Vaulted structures; Folded structures
    • E04B1/3211Structures with a vertical rotation axis or the like, e.g. semi-spherical structures
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32Arched structures; Vaulted structures; Folded structures
    • E04B2001/3223Theorical polygonal geometry therefor
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32Arched structures; Vaulted structures; Folded structures
    • E04B2001/327Arched structures; Vaulted structures; Folded structures comprised of a number of panels or blocs connected together forming a self-supporting structure
    • E04B2001/3276Panel connection details
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04BGENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/32Arched structures; Vaulted structures; Folded structures
    • E04B2001/3294Arched structures; Vaulted structures; Folded structures with a faceted surface

Abstract

A structural system comprising the symmetrical interpenetration of an icosahedron and dodecahedron, further articulated to form a rhombic triacontahedron with each rhombus subdivided by two diagonals at its midpoint. The vertices of the original icosahedron and dodecahedron, and the midpoints of the rhombi, are projected such that a single circumscribed sphere would touch or nearly touch all three sets of resulting vertices. This geometry may used to create a hemispheric geodesic dome. Alternatively, this dome may be subdivided along the hemisphere's great circle segments into two half domes or four quarter domes. Rectangular structural elements may be inserted between the half or quarter domes to increase dome area without increasing dome height and to provide other advantages. The basic triangular components of the disclosed structure may be cut with minimal waste from conventional rectangular construction material such as Structural Insulated Panels. These basic triangular components may be connected with a living hinge.

Description

    CROSS-REFERENCE TO RELATED APPLICATIONS
  • This application claims the benefit of U.S. provisional application “Geodesic triacontrahedron” application No. 60/760,009, filed on Jan. 18, 2006 and is incorporated herein by reference.
  • STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
  • Not Applicable
  • REFERENCE TO A SEQUENCE LISTING
  • Not Applicable
  • BACKGROUND OF THE INVENTION
  • (1) Field of the Invention
  • The invention relates to means and methods of combining two platonic solids, the icosahedron and the dodecahedron, as a dual geometry and further articulating this geometry to form a rhombic triacontahedron with each rhombus subdivided by two diagonals at its midpoint. The vertices of the original icosahedron and dodecahedron, and the midpoints of the rhombi, are projected such that a single circumscribed sphere touches or nearly touches all three sets of resulting vertices. This geometry creates dome-like dwelling designs with unique and useful connection and expansion capabilities. The geometry's single basic triangular component facilitates highly efficient panelized use of prefabricated building materials such as Structural Insulated Panels (SIPs). The invention also relates to means of creating a panel connection system to secure the disclosed panels.
  • (2) Description of the Related Art
  • U.S. Pat. No. 5,628,154 to Gavette discloses a modular system of constructing a spherical icosahedron or dodecahedron. The Gavette dome may be viewed as a collection of pentagons, and deemed a dodecahedron or may be viewed as a collection of triangles, and deemed a hexakis icosahedron. In either case, the panels are constructed as non-planar or curved segments of a sphere.
  • Gavette is not suited for the construction of dome segments from conventional planar or flat surfaced construction components. Gavette uses a plurality of right angle or near right angle triangles formed in aggregate as large curved components. Structural Insulated Panels (SIPs), sheets of plywood, and other widely available and relatively inexpensive construction materials are planar and hence not usable for construction of a Gavette dome.
  • Gavette's integrated ribbing structure or support system also makes Gavette unsuitable for efficient construction of larger structures, Gavette requires curved support components built into curved panels. These larger curved panels are inefficient for efficient storage and shipment. Furthermore, the integrated rib system of Gavette does not allow for the Gavette dome to easily and efficiently integrate doors, windows and other standard building components typical of full scale structures,
  • The preferred and illustrated embodiment of Gavette's dome is an orientation of the basic icosahedron/dodecahedron dual geometry that has ten triangles coming together at its apex. This permits some separation and expansion but not the four way separation and expansion possible with the disclosed design. In addition, Gavette's preferred embodiment precludes a hemispheric dome in favor of an approximate ⅝ dome. The inwardly curving portion of this ⅝ dome near the base makes door and window integration additionally problematic. This ⅝ embodiment, along with his very large basic building components, make the Gavette design efficiently suitable for only relatively small scale structures.
  • Thus, there is a need in the art for means to construct relatively large, full scale dome structures from flat construction stock and to integrate conventional building components such as doors and windows into these dome structures.
  • BRIEF SUMMARY OF THE INVENTION
  • The present invention overcomes shortfalls in the related art by disclosing a dome structure that may be efficiently fabricated with Structural Insulated Panels (SIPs) or other conventional planar building materials. The invention also presents a unique connection system wherein each SIP panel is connected by a spline design using a flexible or living hinge. Unlike Gavette, no internal support system is needed.
  • The invention, sometimes referred to herein as a “geodesic rhombic triacontahedron” or the proposed “geodesic triacontahedron” is a space enclosing structure based upon the dual icosahedron/dodecahedron. The dual of these of these two platonic solids has two sets of vertices, one set for the icosahedron and one set for the dodecahedron. The two sets of vertices are located at different radial lengths from the center of this three dimensional dual. Further refinements of this dual geometry produce a rhombic triacontahedron with each diamond-shaped rhombus subdivided by two diagonals at the midpoint of the rhombus. The vertices of the original icosahedron and dodecahedron, and the midpoints of the rhombi, are projected such that all resulting vertices are of equal radial length from the center of the triacontahedron. A single sphere circumscribing this geometry would touch all resulting vertices.
  • The resulting spherical geometry can be seen as composed of a “weave” of great circles, each of which could subdivide the sphere into two identical hemispheres. The preferred embodiment of this spherical geometry is a dome or hemisphere with a great circle as its base and two great circle segments crossing at its apex. This hemisphere or dome is composed of 60 near right triangles. These basic triangles are identical in interior angles and side lengths, with 30being mirror geometries of the other 30.
  • The basic geometry of the disclosed design produces advantageous resolutions to several of the design limitations inherent in dome architectures based on other geometries. The present invention has the following advantages over the related art: 1) Only one basic triangle is utilized to accomplish geodesic projection, thus reducing manufacturing costs and installation time; 2) All manifestations of the basic geometry are hemispheric domes, thus maximizing the efficiency of enclosed space and building materials; 3) An intersection of two great circle segments at the geometry's apex allows for attractive and efficient rectilinear floor plans; 4) The basic triangle closely approximates a right triangle, thus minimizing costly waste in cutting the triangles from conventional rectangular stock.
  • Unlike prior dome designs, the disclosed geodesic triacontahedron hemisphere can be divided into even halves, and further divided into even quarters. The half dome sections can be separated in one direction and bridged with rectangular elements, and the quarter dome sections can be separated in two directions and bridged with rectangular elements. This separation and bridging creates new geometries that we have termed one direction extension and two direction extension Geodesic Triacontahedron domes.
  • These dome extensions produce several new and advantageous design features not seen in other dome structures. These design features are: 1) increased ratio of enclosed space to the surface area of the dome, 2) increased ratio of enclosed floor area to the height of the dome, 3) the capacity to increase the dome's enclosed space and floor area without increasing the size of the basic triangle, 4) the option for functional segregation of the enclosure based on the extended portion's more rectilinear and utilitarian geometry, 5) increased potential for rectilinear floor plan divisions due to the increased use of great circles segments and the straight joints of the extension panels, and 6) the capacity for an extended half dome to be attached as an addition to conventional rectilinear structures.
  • The preferred embodiment of the disclosed design utilizes Structural Insulated Panels (SIPs) as the material from which the dome triangles are formed. A SIP is a very strong, pressure-laminated building material typically consisting of an outer and an inner face made form an engineered structural board such as Oriented Strand Board (OSB) and an insulating inner core of rigid plastic foam. Although SIP stock with other parameters is manufactured, the preferred embodiment is based on rectangular SIP stock which is 8 feet wide with a thickness varying from 6.5″ to 12.15″ inches. These dimensions, coupled with the basic triangle's close approximation to a right triangle, minimize SIP stock waste, and maximize thermal and building efficiency in most anticipated applications. However, the disclosed design and its extensions are not limited to these SIP parameters, or even to SIP utilization in general.
  • Two different cutting patterns are used to generate the proposed basic triangle in two different sizes. Thus, these two cutting patterns generate two hemispheric domes of differing diameters. Due to their thickness, the basic triangles generated from SIP stock are “beveled” in order to fit together to form the proposed Geodesic Triacontahedron dome.
  • The use of SIPs to implement the proposed Geodesic Triacontahedron dome and its extensions produces the advantageous and synergetic interaction of three factors. These factors are: 1) The strength to weight ratio of the SIP surpasses that of conventional building materials and ideally matches the parameters of the proposed domes and their extensions; 2) The beveled edges of the insulated triangles, along with the relatively few number of components required to construct the dome, ensure extreme thermal efficiency; 3) The single installation of a triangular SIP in the proposed design replaces the “stick-built” tasks of framing, sheathing and insulating, thus saving a substantial amount of labor.
  • The use of near right triangles makes Structural Insulated Panels or SIPs an economical alternative to traditional building materials. The thickness of the SIPs requires that each triangular panel be beveled in order to fit together to form the geometry of the invention. Each edge of the triangular panel has a different dihedral angle of approximately 2, 20, or 30 degrees.
  • The three different dihedral angles and the related beveling necessary to accommodate the various angular interfaces for all possible pairs of adjacent panels present unique challenges for panel construction. These challenges are solved by the disclosed connection system that uses a spline design with a flexible or living hinge. The splines are extruded in lengths to match the length of all possible joints between adjacent panel edges.
  • A hub system is also disclosed to speed installation time and to make construction of the dome safer. These designed hubs are welded steel and all sixty of the dome triangles are connected to these hubs. The resulting increase in structural integrity makes the dome panels securely connected to each other and to the ground. These hubs also are part of the temporary support system during assembly to support the partial dome until all components are in place and the dome is self-supporting.
  • These and other objects and advantages will be made apparent when considering the following detailed specification when taken in conjunction with the drawings. FIGS. 11, 12, 13, 14, 15, 16, 17, 18, 26, and 27 are subject to copyright protection held by Michael Thompson Morley.
  • BRIEF DESCRIPTION OF THE DRAWINGS
  • FIG. 1 is a perspective view of an Icosahedron solid.
  • FIG. 2 is a perspective view of a Dodecahedron solid.
  • FIG. 3 is a perspective view of an Icosa/Dodeca dual.
  • FIG. 4 is a perspective view of a Rhombic Triacontahedron.
  • FIG. 5 is a perspective view of a Subdivided Rhombic Triacontahedron.
  • FIG. 6 is a perspective view of a Geodesic Rhombi Triacontahedron with vertices projected in accordance with the principles of the invention.
  • FIG. 7 is a perspective view of a hemisphere in accordance with the principles of the invention.
  • FIG. 8 is a perspective view of the dome in accordance with the principles of the invention with a stem wall and an extension bridging the great circle segments.
  • FIG. 9 is a perspective view of the dome in accordance with the principles of the invention with a stem wall and an extension raising above the great circle segments.
  • FIG. 10 is a perspective view of the disclosed geometry.
  • FIG. 11 is a perspective view of a Structural Insulated Panel or SIP
  • FIG. 12 is a perspective view of a panel connection assembly.
  • FIG. 13 is an exploded view of a panel connection assembly.
  • FIG. 14 is an exploded view of a hub assembly.
  • FIG. 15 to FIG. 18 are plan views of basic triangles used to construct the dome structures in accordance with the principles of the invention.
  • FIG. 19 is a top view of a hemisphere in accordance with the principles of the invention.
  • FIG. 20 is a front view of a hemisphere in accordance with the principles of the invention.
  • FIG. 21 is a top view of two half domes moved apart with extension elements added in accordance with the principles of the invention.
  • FIG. 22 is a front view of two half domes moved apart with extension elements added in accordance with the principles of the invention.
  • FIG. 23 is a top view of four quarter domes moved apart with extension elements added in accordance with the principles of the invention.
  • FIG. 24 is a front view of four quarter domes moved apart with extension elements added in accordance with the principles of the invention.
  • FIG. 25 is a plan view of spline design.
  • FIG. 26 is a plan view of cutting patterns used on flat construction material in accordance with the principles of the invention.
  • FIG. 27 is a plan view of splines in place.
  • DETAILED DESCRIPTION OF THE INVENTION
  • The following detailed description is directed to certain specific embodiments of the invention. However, the invention can be embodied in a multitude of different ways as defined and covered by the claims. In this description, reference is made to the drawings wherein like parts are designated with like numerals throughout. Unless otherwise noted in this specification or in the claims, all of the terms used in the specification and the claims will have the meanings normally ascribed to these terms by workers in the art.
  • The Basic Geometry
  • Platonic solids are three-dimensional geometries in which each face of the particular solid is identical to all the other faces. In addition, the angles of each face and the length of each face edge are identical. In other words, each platonic solid is symmetrical in every way possible. The platonic solids are the: tetrahedron, octahedron, cube, icosahedron, and dodecahedron.
  • Buckminster Fuller used some of the platonic solids as the basis for his development of the geodesic dome. In the geodesic dome the faces of a platonic solid are triangulated. Both the vertices of the original platonic solid and the new ones formed by the face triangulation are centrally projected to a theoretical sphere. This imaginary sphere circumscribes the original platonic solid, touching both the original and new vertices in what can be termed a geodesic projection.
  • The most well-known and utilized of Fuller's geodesic domes is constructed as described above, using the icosahedron as the base platonic solid, and geodesic triangulation of each icosahedron face as the method of practical implementation
  • Problems with Conventional Geodesic Domes
  • Conventional geodesic domes produced from the icosahedrons have an attractive appearance, but suffer from several practical restrictions. Some of these design limitations are discussed below:
  • Complexity of triangulation—Even the simplest geodesic triangulation of each icosahedron face typically requires two different triangles, each with its own size and angles. This added complexity increases construction cost and installation time.
  • Hemisphere configuration—Hemispheric domes generally offer the most efficient use of building materials and enclosed space. However, before a truly spherical hemispheric dome can be generated, triangulation of each icosahedron face must become much more complex, requiring several different triangles.
  • Interface with interior walls—Efficient residential floor plans are generally derived from primarily rectilinear room divisions. Conventional geodesic domes are constructed from triangles that join to create non-continuous lines and non-rectilinear line patterns. Therefore, it is nearly impossible for such domes to have rectilinear floor plans with interior walls that interface efficiently and attractively with the undersurface of the dome's triangulated shell.
  • Cutting pattern efficiency—Geodesic projections for conventional domes create triangles that are all nearly equilateral. Virtually all building materials used to construct a conventional dome's component triangles are cut from rectangular stock. Since equilateral triangles overlay very inefficiently on rectangles, a conventional dome's component triangles are typically obtained only by wasteful and costly cutting patterns.
  • The disclosed design solves many of the limitations of the icosahedron-based geodesic dome, and creates new and very advantageous capacities never seen in any prior space-enclosing geometry.
  • The Rhombic Triacontahedron
  • In solid geometry when the structures interpenetrate each other in symmetrical manner the resulting structure is called a “dual.” An icosahedron/dodecahedron dual FIG. 3 is formed when 1) each edge of the icosahedron crosses, at right angles, an edge of the dodecahedron at their respective midpoints, 2) each vertex of the icosahedron is centered above the planar surface of one of the dodecahedron's faces, and 3) each vertex of the dodecahedron is centered above the planar surface of one of the icosahedron's faces.
  • Two spheres can be circumscribed around the icosahedron/dodecahedron dual, one touching the original icosahedron's vertices, and one touching the original dodecahedron's vertices. Each sphere has a different radius from the center of the three-dimensional dual icosahedron/dodecahedron geometry.
  • The right angle intersection of each icosahedron edge with a dodecahedron edge defines a diamond-shaped plane called a rhombus FIGS. 3-5, 1. These diamond-shaped rhombic planes form a three dimensional structure called a rhombic triacontahedron FIG. 4. This is the original icosahedron/dodecahedron dual with each vertex of the dodecahedron connecting to three adjacent vertices of the icosahedron. A sphere that would touch the mid-point of each rhombic plane, where an icosahedron edge and a dodecahedron edge intersect, would not circumscribe but would actually be located inside the rhombic triacontahedron. This sphere would have a radius from the center of the rhombic triacontahedron that is different from the radii of either of the first two spheres described above.
  • The Invention, the Geodesic Triacontahedron
  • In the description above, we have defined three sets of vertices for the proposed geometry. Set 1 consists of the vertices of the original icosahedron FIG. 10, 2. Set 2 consists of the vertices of the original dodecahedron FIG. 10, 3 and, Set 3 consists of the midpoints of the rhombic planes FIG. 10, 4 of the derived rhombic triacontahedron. Each of these three sets is at a different radial distance from the center of the dual icosahedron/dodecahedron (now a rhombic triacontahedron). In the proposed geodesic geometry, FIG. 6, the radial distance from the center of the three dimensional rhombic triacontahedron is made consistent for all three sets, so that a single circumscribed sphere touches all resulting vertices in all three of these sets. This proposed geometry has 62 vertices, 120 triangular faces and 180 edges. It is an efficient approximation of the circumscribed sphere, as all 120 triangles have the same angles and size, with 60 triangles being mirror images of the other 60. We have chosen to call this figure a Geodesic Triacontahedron.
  • The primary elements of the proposed design are the parameters for the basic triangle FIG. 10, 5 that forms this geodesic geometry. FIG. 26 is a plan view of two sizes of the basic triangle as cut from Structural Insulated Panels (SIPs), or other similar rectilinear stock. FIGS. 15, 16, 17 and 18 depict the angles and dimensions of these two size variations of the basic triangle.
  • A key characteristic of the proposed geometry is that the edges of contiguous triangles form only great circles. A great circle is a continuous straight line extending across the surface of a sphere which, like the equator of the earth, cuts the sphere into two equal hemispheres. Thus, the original geometric triacontahedron divides evenly into two equal hemispheres along any of this geometry's great circles. This is a characteristic that most of the less complex icosahedron-based geodesic domes do not have. As hemispheric domes typically represent the most efficient use of materials and interior space, this is an important functional consideration.
  • Once a hemisphere is created from the original triacontahedron sphere and positioned with its “equator” on the ground or a flat base, the top view of this structure reveals segments of two of the original great circles intersecting at right angles at the hemisphere's apex FIG. 19, 6 where 7-8 and 9-10 show two great circles interesting at point 6. These great circle segments have the functional properties of complete great circles and, for simplicity, are referred to herein as “great circles”. The intersection of these two great circles gives the proposed design certain advantages over conventional domes, as described below. This great circle intersection also serves as the basis for “extensions” of the basic proposed geometry, as further described below.
  • Advantages of the Invention
  • As stated before, conventional geodesic domes constructed from icosahedron-based geometry suffer from several design restrictions. The basic geometry of the proposed design resolves these design limitations, as described below:
  • Complexity of triangulation—As opposed to the conventional geodesic dome, the proposed design accomplishes geodesic projection with only one basic triangle. No matter what its size, the basic geometry of the proposed design is comprised of only sixty of these triangles (30 being mirror images of the other 30). This design simplicity reduces construction costs and installation time.
  • Hemisphere configuration—As opposed to conventional geodesic domes, all manifestations of the basic geometry are hemispheres, which typically offer more efficient use of building materials and space than any other dome configuration.
  • Interface with interior walls—As opposed to the “broken” and non-rectilinear joint patterns of conventional geodesic domes, two straight great circles intersect at right angles at the apex of the Geodesic Triacontahedron dome. Interior walls can be “dropped” from the undersurface of the dome's shell anywhere along each straight and continuous great circle. Such walls interface attractively and efficiently with the dome's undersurface. In addition, because interior walls can follow both of the great circles intersecting at 90 degrees, a large variety of predominately rectilinear floor plans can be generated.
  • Cutting pattern efficiency—As opposed to the conventional geodesic dome's nearly equilateral component triangles, the basic triangle used to accomplish geodesic projection for the proposed design closely approximates a right triangle, distorted only slightly from 90 degrees for the spherical application. Since right triangles overlay rectangular building material stock very efficiently, cutting patterns that minimize waste and cost are obvious. FIG. 26 shows examples of such efficient cutting patterns.
  • Dome Extensions
  • The proposed Geodesic Triacontahedron dome with two great circles intersecting at right angles at the hemisphere's apex is depicted in FIG. 19, 6. The hemisphere can be subdivided into two “half domes” along either of these great circles. These half domes can then be moved apart and rectangular structural elements inserted to bridge the space between the triangles on each half dome that were adjacent before this separation. This can be thought of as a single extension of the Geodesic Triacontahedron dome, as the dome is extended in a single direction FIG. 21 and FIG. 22.
  • Dividing the original hemispheric dome into four-quarter domes along intersecting great circle creates the second variation of the Geodesic Triacontahedron dome. The four-quarter domes are moved apart in two directions and rectangular structural elements are inserted to bridge the space between the triangles on each quarter dome that were adjacent before this separation. This can be thought of as a double extension of the Geodesic Triacontahedron dome, as the dome is extended in two directions FIG. 23 and FIG. 24.
  • Advantages of Dome Extensions as used with the Invention
  • Some of the more complex icosahedron-based geodesic domes can be constructed as hemispheres. But none of these icosahedron-based domes can be “halved” or “quartered” in the way that the Geodesic Triacontahedron dome can be sectioned and extended. The extension variations of the basic Geodesic Triacontahedron dome give it distinct advantages over the conventional geodesic dome. Some of these advantages are:
  • Increased space enclosure—The “stretched” portion of the extended Geodesic Triacontahedron dome can be considered vaulting. Such vaulting encloses more space per unit of external surface area than the triangulated or domed portion of the structure. Thus, the overall space enclosed per unit of external surface area is increased. The rectangular structural elements are less costly to produce than the triangular elements. Thus, the cost per unit of enclosed space is reduced.
  • Increased space utility—The typical way to increase useable floor area in a conventional icosahedron-based geodesic dome is to increase the diameter of the dome. However, this automatically increases the dome's height. This height increase encloses more vertical space, which often cannot be utilized efficiently on the first floor and does not add sufficient height to permit a second floor. The end result is more construction costs and more unused space to heat/cool. The Geodesic Triacontahedron dome can be extended in increments to increase first floor area without increasing the overall height of the dome.
  • Consistent size of dome triangles—As discussed above, conventional icosahedron-based geodesic domes are increased in diameter to enclose more floor space. When this occurs, the triangular components of the dome must either increase in size, or the number and variety of triangular components must increase. In either case this can increase construction and installation costs. On the other hand, the Geodesic Triacontahedron dome's triangular components are all composed from the same shape (or its mirror image). When this dome is extended as described above, its floor space increases, but the size of its triangular components remains the same. This has important implications for manufacturing and installation as further described herein.
  • Optional segregation of function—A dome's shell is typically constructed from flat triangles that are joined at angles. From inside the dome, the dome's shell can be seen as angling in two directions—left/right and up/down. This two-way curvature is the reason that domes do not easily conform to rectilinear standards for exterior doors, windows, furniture, cabinetry, countertops, home appliances, etc. However, the Geodesic Triacontahedron's vaulted dome extensions curve in only one direction—up/down. Thus, the single-curve of dome extensions is much more “rectilinear friendly” than the dual-curving dome shell.
  • This distinction promotes a natural segregation of function, with the more work-oriented areas located under the vaulted dome extensions, and the more leisure-oriented areas located under the dome shell. Following this functional segregation, many rectilinear building and furnishing components, such as exterior doors, countertops and large appliances, would be located in the vaulted extension.
  • The proposed Geodesic Triacontahedron dome and its optional extensions are designed to create a highly efficient space-enclosing structure. Many possible applications will be found for these structures, with most of these uses revolving around human-oriented living and/or working space. Such uses may include home construction, churches, grade schools, small industrial buildings, temporary disaster housing, and remote research station construction.
  • The optional segregation of function that dome extensions provide might be applied to a large number of these possible applications. For example, in a single extension Geodesic Triacontahedron home the living and dining areas might be located in one dome end with the master bedroom and bath located in the other dome end. The kitchen, laundry area, children's bedrooms and baths would be located in the middle, vaulted extension section. A larger extended dome might used as a small grade school with classrooms located in the middle vaulted area, and the two half domes enclosing a gym/auditorium at one end and a cafeteria at the other. When used as a research station, the extended dome's vaulted section might enclose the research area, with a dormitory under one half dome and a common eating/social area under the other half dome.
  • Interface with interior walls—As noted earlier, the shells of most conventional domes lack great circles. Consequently, these structures typically lack a clean interface between the undersurface of the dome's triangulated shell and the dome's interior walls. The basic geometry of the proposed Geodesic Triacontahedron dome resolves this design problem by “dropping” straight interior walls or wall sections from the dome shell's great circles. If all of the space below these two great circles were to be utilized as interior walls, the dome could be seen as having two long straight walls, with each wall completely bisecting the dome's base and each wall intersecting the other wall at 90 degrees, FIG. 19, lines 7-8 & 9-10.
  • A single extension of the basic geometry increases the length of the top of one the great circles by exactly the length of the extension itself FIG. 21, line 11-12. At 90 degrees to this lengthened great circle, a third great circle is formed FIG. 21, line 13-14. Additional interior walls can be dropped from both the great circle extension and the third great circle. Furthermore, two of the seams connecting the rectangular extension panels are high enough on the dome to allow interior walls to be dropped from them FIG. 21, line 15-16 & 17-18.
  • A double extension of the basic geometry creates four great circles, each one lengthened by the length of the extension. Interior walls can be dropped from these extended great circles, as well as from the four extension panels seams just below the intersections of the four great circles FIG. 23 and FIG. 24.
  • Well-designed floor plans might not utilize every opportunity for interior walls provided by great circles, great circle extensions and extension panel seams. However, the descriptions above illustrate that the proposed dome extensions promote clean and efficient interfaces between the dome shell and the dome's interior walls. Thus, these dome extensions significantly increase the degree to which rectilinear floor plans, and other rectilinear conventions, can be utilized with the proposed design.
  • Interface with conventional construction—The conventional icosahedron-based geodesic dome cannot be evenly sectioned to serve as an attachment or addition to conventional rectilinear buildings. As described above, the disclosed design can be “halved” evenly. A half dome (one quarter of the whole geometric sphere) can be easily attached to a conventional structure which has a vertical wall height higher than the apex of the half dome. Dome extensions often increase the size and/or functionality of such an addition. For example, a single extension, as described above, could attach a half dome to the rear of a conventional home to create an elegant master bedroom suite.
  • The preferred geometric embodiment of the disclosed design is described in detail in the preceding sections. In summary, this geometric embodiment comprises a subdivided rhombic triacontahedron with the vertices of its component icosahedron and dodecahedron, and the midpoints of its component rhombi, projected to all touch a theoretical circumscribed sphere. This can be termed a geodesic geometric solution. The hemispheric dome derived from this basic geometry has many practical advantages that are derived from 1) its inherent great circle segments, and 2) its near right angle basic component triangles. It is to be noted that non-geodesic approximations of this basic geometry might be created that would also form great circle segments and near right angle basic component triangles. In such non-geodesic geometric solutions all the vertices might not touch a circumscribed sphere. These non-geodesic solutions are included in this general design as non-preferred geometric embodiments.
  • The Preferred Construction Embodiment—Structural Insulated Panels (“SIPs”)
  • The proposed Geodesic Triacontahedron dome and its extensions are designed as space-enclosing structures which can be constructed from a variety of building materials using several building techniques. Many of the materials and techniques used to construct conventional icosahedron-based geodesic domes might also be used to construct the proposed design. Such materials might include plywood or pressboard exteriors and drywall interiors. Building techniques might include prefabrication of the triangular and rectangular components or fabrication “on-site.” The components might fit together directly using a variety of connectors. Or, a “hub-and-strut” shell might be constructed using metal hubs and wood struts. The triangular and rectangular components could then be attached to this geometric framework.
  • Though the disclosed design can utilize many of these alternatives, there is one building material that is seen as the most efficient and elegant match for the proposed geometries. This material is the Structural Insulated Panel (SIP). The following description outlines a preferred embodiment of the disclosed design using Structural Insulated Panels. However, description of this preferred embodiment should not be viewed as limiting the overall potential of the disclosed design to be utilized with other building materials and building techniques.
  • A SIP comprises of two outer skins and an inner core of an insulating material which has been pressure-laminated together. When properly bonded, these three components act synergistically to form a composite that is much stronger than the sum of its parts. The outer skins typically consist of Oriented Strand Board, though plywood or other materials are sometimes used. The core of SIPs can be made from a number of materials including molded expanded polystyrene, extruded polystyrene and urethane foam. Stock SIPs are produced in thicknesses from 4.5 inches to 12.25 inches and in sizes from 4 feet by 8 feet up to 9 feet by 30 feet.
  • Advantages of SIP Embodiment
  • The SIP is envisioned as the preferred embodiment for the proposed Geodesic Triacontahedron dome because of the strength, thermal efficiency and labor-saving economy that this building material will bring to the implementation of the disclosed design. These three factors are discussed below:
  • SIP strength—Structural Insulated Panels meet the structural requirements of all the major building codes. The axial, transverse and racking load capabilities of these panels will give this dome strength to weight ratios unavailable with conventional building methods. All of the spans generated by each size configuration of the dome triangles are well within the structural limits of the panels, and, like an “I” beam, the strength of the SIP panel increases as its cross-sectional depth or thickness increases. Therefore, under extreme weather conditions or special architectural requirements, a thicker cross section would be specified. This capacity for SIP strength to be increased makes it a perfect match for the design flexibility of the proposed dome design and its extensions.
  • SIP thermal efficiency—The insulating cores of the panels offer very high R-values per inch of material, and the small number of pieces required to complete the structure results in fewer seams and a much tighter structure compared to conventional buildings. In addition, the method of finishing and joining the triangles' edges, as described below, creates a structure with no thermal bridging except next to doors and windows.
  • SIP labor-saving economy—The installation of a three-layer laminated SIP takes the place of three separate “stick-built” operations. In a single installation procedure the tasks of framing, sheathing and insulating are eliminated, thus saving a substantial amount of labor. The inherent labor-saving economy of SIP installation is substantially increased with the proposed design, given the fact that only 60 triangles are assembled. This is compared to many hundreds of pieces required to frame a conventional geodesic dome or a conventional “stick-built” home.
  • SIP Cutting Patterns
  • The SIP is presented in this disclosure as the preferred embodiment of the disclosed design. This should not be viewed as limiting the disclosed design to being constructed with SIPs. In addition, an extremely efficient utilization of the SIP is presented below as the preferred embodiment of the SIP-based Geodesic Triacontahedron dome. This should not be viewed as limiting the disclosed design to the cutting patterns, the cut SIP size, or the dome diameters described below. Rather, these descriptions should be seen as illustrating the efficiency and synergetic potential of using SIPs to construct the disclosed design.
  • Over the last few years the SIP industry has evolved to the point where certain standards are well-established. One of these is the standard size of the SIPs. Almost all SIP manufacturers produce SIPs with a minimum width of 8 feet, and a maximum size of 9 feet ×30 feet. Though SIPs wider than 8 feet do exist, 8 feet is most common SIP width and is used as a standard in these calculations. However, the disclosed design should not be considered to be limited to 8 foot wide SIP material.
  • The width of the panels is the key factor in orienting the basic triangle on rectangular SIP stock to produce various cutting patterns. Orienting the basic triangle's hypotenuse along the 8 foot SIP width produces a very inefficient cutting pattern and a very small dome diameter. This alternative will not be considered. However, orienting either of the triangle's shorter sides along the 8 foot SIP width produces extremely efficient cutting patterns. This is due to the fact that either of these orientations takes advantage of the triangle's near right angle. These orientations allow cutting patterns that are, in essence, a series of near-rectangular parallelograms that minimize SIP cutting waste, FIG. 26. 19 of FIG. 26 shows the minimal areas of waste, while 20 shows optional panel truncation to allow for skylights and greater panel size.
  • By alternately orienting each of the triangle's two short sides along the 8 foot SIP width, two basic cutting patterns are generated. Each basic pattern produces a different-sized triangular component, which in turn produces a dome with a particular diameter and enclosed square footage.
  • Panel Connections
  • The thickness of the SIP, as described above, requires that each triangular panel be “beveled” in order to fit together to form a structurally-sound Geodesic Triacontahedron dome. Each edge of the triangular panel will have a different dihedral angle.
  • Making such precise beveled cuts in SIP panels has been made possible only very recently by the development of expensive computerized European saws installed in the last three years in a handful of American SIP manufacturing plants. This technology is literally at the cutting edge of the SIP industry and enables the manufacture of the proposed triangular panel as an extremely efficient, low-cost building material.
  • Given the necessary triangular shape and beveled edges of the proposed SIP panels, connecting these panels presents unique challenges. The invention's connecting design utilizes a “spline” design based on a formula composite manufactured from extruded PVC or a foamed polypropylene. The splines are extruded in lengths to match the length of all possible joints between adjacent panel edges.
  • The structural connections between triangles are made when a spline is inserted into slots in the foam under the exterior and interior skins of adjacent SIP panels, FIG. 27, 21. These slots, which are pre-cut during the manufacturing process, are made slightly larger than the splines for ease of installation. After installation, the splines are pulled into their final position with screws, drilled through the exterior of the skins and screwed into the splines, pulling the splines tight up against the inside of the skin FIG. 27, 22.
  • Three different angles (approximately 2 degrees, 20 degrees, and 30 degrees) are used to accommodate the various angular interfaces for all possible pairs of adjacent panels, FIG. 27. Ideally one spline design could be utilized to connect all possible pairs of adjacent panels despite their differing angular interfaces. FIG. 25A, 25B, and 25C show two possible methods of extruding the splines with a living hinge. In these methods the splines are extruded as a composite incorporating reinforcing threads or pieces. In the first method, FIG. 25A the splines are extruded with a living hinge created by the extrusion process. In this method, the reinforcing material is evenly distributed throughout the spline.
  • In the second method, FIG. 25B the spline is extruded without a living hinge. The living hinge is created as a second step when the previously extruded spline is compressed or stamped, FIG. 25C. This method has the possible advantage of having relatively more reinforcing material concentrated in the area of the living hinge where added strength may be useful. In contrast, the wider portions of the spline have relatively less reinforcing material. This may allow the screws drilled through the skins of the SIPs to more easily penetrate the wider portions of the splines.
  • While this panel connection system is designed to connect the basic components of the proposed Geodesic Triacontahedron design, it has wider applications. The disclosed panel connection system could be used in many construction situations where two SIPs need to be attached to each other at angles less than approximately 180 degrees but greater than approximately 90 degrees.
  • Foundation Connections
  • The base course of SIP panels is connected to the foundation by attaching the bottom of the first course panels to the foundation or floor deck. To accommodate the base plate, the edge foam is relieved from the bottom face of the base panel to the depth of the base plate. When panels are installed on concrete or on other material not compatible with wood, a base plate assembly is bolted to the foundation by code approved connection methods and the SIP triangle is connected to the plate with screws attached horizontally.
  • Hubs and Jigs
  • As noted previously, the eight-foot width of the standard manufactured rectangular SIP panel sets the parameters for very efficient triangular panel cutting patterns. However, by truncating the acute ends of these triangles, larger panels can be cut from the same standard rectangular SIP FIG. 26, 20. FIG. 11 shows an 8×24 foot SIP cut into the disclosed near right triangles and used to construct the disclosed structure. The space created by the truncating of the triangles leaves room for a structural hub that greatly strengthens the dome. The hubs are also used to help stabilize the dome during assembly before the dome becomes stable when all pieces are in place. The designed assembly jig aligns, supports and stabilizes the structure.
  • FIG. 12 shows panel connection details. FIG. 13 and FIG. 14 show hub and spline details.

Claims (18)

1. A building structure comprising a plurality of two sets of near right angle component triangles, with each set a mirror image of the other, such that the vertices of the structure are all of equal radial distance from the center of the structure, thus creating a structural approximation of a hemisphere with great circle segments crossing at the apex of the hemisphere.
2. The building structure of claim 1 wherein the vertices correspond to a subdivided rhombic triacontahedron such that vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are projected so that all three resulting sets of vertices are of equal radial distance from the center of the structure.
3. The building structure of claim 2 wherein the vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are of unequal radial distance from the center of the structure but are close enough to equal distance to produce near right angle component triangles which can be cut efficiently (less than 15% material cutting waste) from rectilinear building materials.
4. The building structure of claim 2 wherein the vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are of unequal radial distance from the center of the structure but are close enough to equal distance to produce a close approximation of a hemisphere with great circle segments crossing at the apex of the hemisphere.
5. The building structure of claim 3 wherein the intersection points of the rhombi diagonals are projected to a radial length between the radius length of the icosahedron and the radius length of the dodecahedron.
6. The hemisphere structure of claim 2 subdivided into two half domes along either of the hemisphere's great circle segments.
7. The two half domes of claim 6 moved apart.
8. The two half domes of claim 7 with rectangular structural elements inserted between the two half domes.
9. The two half domes of claim 6 subdivided into four quarter domes along the remaining great circle segments of the original hemisphere.
10. The four quarter domes of claim 9 moved apart.
11. The four quarter domes of claim 10 with rectangular structural elements inserted between the four quarter domes.
12. The building structure of claim 1 constructed from structural insulated panels (SiPs).
13. The building structure of claim 1 comprising a basic spherical geometry comprising 62 vertices, 120 triangular faces and 180 edges, with all 120 triangular faces having the same angles and size, with 60 of the triangular faces being mirror images of the other 60 triangular faces.
14. The building structure of claim 12 wherein the triangular SIPs are beveled.
15. The panels of claim 14 wherein each edge of a panel has a different dihedral angle.
16. The panels of claim 15 wherein each edge of a triangular panel is approximately 2 degrees, 20 degrees and 30 degrees.
17. The panels of claim 16 connected together with a spline comprising a living hinge.
18. The spline of claim 17 fixed in three separate angles of approximately 2 degrees, 20 degrees, and 31 degrees.
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US20120204496A1 (en) * 2011-02-16 2012-08-16 John Patrick Mcsweeney Building panel module, spherical shell and method for making the same
CN102888991A (en) * 2012-10-25 2013-01-23 南通纺织职业技术学院 Large-scale profile steel beam and concrete combined house roof constructing method
US20150037766A1 (en) * 2013-08-02 2015-02-05 The Regents Of The University Of California Convex equilateral polyhedra with polyhedral symmetry
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USD768031S1 (en) * 2015-07-09 2016-10-04 Kheper Games, Inc. Faceted sphere
USD789777S1 (en) * 2014-11-13 2017-06-20 Unique Fine Fabrics Import Inc. Curtain rod finial

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