Apparatus for making a geodesic shape and methods of using the same

A method of making a geodesic shape is provided. The method comprises of providing and assembling a plurality of pre-made forms, and a plurality of struts. The pre-made forms have a triangular shape, first and second inner edges, and an outer edge. The length of each inner edge and outer edge are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere. Using the pre-made forms and struts, a polygonal shape is assembled, each shape having either five or six pre-made forms. The resulting desired polygonal shape and additional desired polygonal shapes made using the same steps are connected at preset angles in known geodesic form and function. The desired polygonal shapes then combine to form a desired geodesic shape. Throughout the process, no struts are operably coupled to other struts.

1. FIELD OF THE INVENTION

The present invention relates generally to the assembly of a Geodesic Dome such that the Geodesic form may be arrived at spontaneously, having achieved the multitude of precise axial and dihedral angles through the use of strategically placed hinges.

Geodesic domes and other geodesic shapes are used in construction as efficient, fast, structurally sound designs. However, a common problem with many methods of assembling geodesic shapes is the need to achieve correct radial, dihedral and axial angels in construction and assemble of the components. Therefore, there is a need for a method of making a geodesic shape out of pre-made forms and struts through the use of hinges attaching struts to their respective panels.

SUMMARY OF THE INVENTION

A first aspect of the present invention provides a method of making a geodesic shape. The method comprises of providing and assembling a plurality of pre-made forms, and a plurality of struts. The pre-made forms have a triangular shape, first and second inner edges, an inner face and an outer face and an outer edge. The length of each inner edge and outer edge are determined by the frequency of the geodesic shape, diameter of the geodesic shape, using known formulas for relating diameter and frequency when creating a geodesic dome or sphere. Using the pre-made forms and struts, a polygonal shape is assembled in several steps. The first step comprises operably coupling a first pre-made form, along its uncoupled first inner edge to a first face of a first strut, by a first hinge(s). The second step comprises operably coupling a second of the pre-made form, along its uncoupled second inner edge to a second face of the first strut, by a second hinge(s). The third step comprises operably coupling the second pre-made form, along its uncoupled first inner edge to a first face of a second strut, by a its first hinge(s). The fourth step comprises sequentially operably coupling inner edges of additional pre-made forms to respective faces of struts already in the structure and sequentially operably coupling additional struts to the additional pre-made forms in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms have not been coupled to respective faces of the last additional strut. The fifth step comprises forming the desired polygonal shape by operably coupling the inner edge of a last coupled pre-made form and a second inner edge of the first premade form to respective faces of the last additional strut, creating desired dihedral angles between the inner edges of the pre-made forms, and creating a desired axial angles between a z axis of the desired polygonal shape and the inner face of each premade form. The total number of pre-made forms in the polygonal shape is either four five or six. In addition to polygonal shapes there are also polygonalpatch(es). There is a method for assembling a polygonal patch. The first step of the method involves operably coupling a seventh pre-made form, along its uncoupled first inner edge to a first face of a seventh strut, by a first hinge(s). A second step involves operably coupling an eighth pre-made form, along its uncoupled second inner edge to a second face of the seventh strut, by a second hinge(s). A third step involves operably coupling the eighth pre-made form, along its uncoupled first inner edge to a first face of an eighth strut, by its first hinge(s). A fourth step involves operably coupling a ninth pre-made form, along its uncoupled second inner edge to a second face of the eighth strut, by its second hinge(s). There is a method for assembling a geodesic shape. The method involves coupling desired polygonal shapes made using the aforementioned steps to desired polygonal shapes, premade forms and to polygonal patches made using the aforementioned steps by coupling their outer edges, so that the desired polygonal shapes, polygonal patches and additional pre-made forms create a geodesic shape. Throughout the entire method, no struts are operably coupled to other struts. Throughout the entire method, the free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user.

A second aspect of the present invention provides an apparatus for making a polygonal shape. The apparatus is comprised of five or six struts each with a first face operably coupled to a first hinge(s) and second face operably coupled a second hinge(s), and five or six pre-made forms which are triangular in shape, with first and second inner edges, an inner face and an outer face, and an outer edge. The lengths of each inner edges and the outer edge of the pre-made form are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency to create a geodesic dome. A first pre-made form is operably coupled along its first inner edge to the first face of a first strut by first hinge(s). A second pre-made form is operably coupled along its second inner edge to a second face of the first strut, its second hinge(s). The second pre-made form is then operably coupled along its first inner edge to a first face of a second strut, by its first hinge(s). A third pre-made form is then operably coupled along its second inner edge to the second face of the second strut by its second hinge(s). The third pre-made form is operably coupled along its first inner edge to a first face of a third strut, by its first hinge(s). A fourth pre-made form is operably coupled along its second inner edge to a second face of the third strut, by its second hinge(s). The fourth pre-made form is operably coupled along its first inner edge to a first face of the fourth strut, by its first hinge(s). A fifth pre-made form may be operably coupled along its second inner edge to a second face of the fourth strut, by its second hinge(s) if there is a sixth pre-made form. The fifth pre-made form may be operably coupled along its first inner edge to a first face of the fifth strut, by its first hinge(s) if there is a sixth strut. A desired polygonal shape is formed by operably coupling the inner edge of a final pre-made form and a second inner edge of the first premade form to respective faces of the last additional strut, creating desired dihedral angles between the inner edges of the pre-made forms, and creating a desired axial angles between a z axis of the desired polygonal shape and the inner face of each premade form. Throughout creation of the desired polygonal shape, no struts are operably coupled to other struts. The free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user.

A third aspect of the present invention provides a method of making a geodesic shape. The method includes a plurality of triangular pre-made forms having a triangular shape, first and a second inner edges, and an outer edge. The length of each inner edge and outer edge are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere. The method includes steps for assembling a polygonal shape. The first step involves operably coupling a first pre-made form, along its uncoupled first inner edge to the first face of a first partial strut, by its first hinge(s). The second step involves sequentially operably coupling inner edges of the first pre-made form to respective faces of partial struts. The third step involves operably coupling a second pre-made form, along its uncoupled inner edges to respective faces of partial struts. The fourth step involves operably coupling the first partial strut of the first pre-made form to the first partial strut of the second pre-made form in a fixed interface forming a complete strut, thus allowing a free range of motion of each strut-panel interface of each panel along its axis. The fifth step involves sequentially operably coupling partial struts operably coupled to inner edges of additional pre-made forms to respective partial struts already in the structure and sequentially operably coupling additional partial struts to the additional pre-made forms in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms have not been coupled. The desired polygonal shape is formed by operably coupling a partial strut operably coupled to an inner edge of a last coupled pre-made form and a partial strut operably coupled to a second inner edge of the first premade form in a fixed interface forming a complete strut, creating desired dihedral angles between the inner edges of the pre-made forms, and creating desired axial angles between a z axis of the desired polygonal shape and the inner face of each premade form. The total number of pre-made forms in the polygonal shape is either five or six. The method includes steps for assembling a polygonal patch. The first step involves operably coupling a seventh pre-made form, along its uncoupled first inner edge to a first face of a seventh strut, by a first hinge(s). The second step involves operably coupling an eighth pre-made form, along its uncoupled second inner edge to a first face of an eighth strut, by a second hinge(s). The third step involves operably coupling the seventh strut and the eighth strut. The fourth step involves operably coupling the eighth pre-made form, along its uncoupled first inner edge to a first face of a ninth strut, by its first hinge(s). The fifth step involves operably coupling a ninth pre-made form, along its uncoupled second inner edge to a first face of a tenth strut, The sixth strut includes operably coupling the ninth strut and the tenth strut. The method includes steps for assembling a geodesic shape. The first step includes coupling desired polygonal shapes made using the previously described steps to desired polygonal shapes, premade forms, and to polygonal patches made using the previously described steps by coupling their outer edges at preset angles in known geodesic form and function, so that the desired polygonal shapes, polygonal patches, and additional pre-made forms create a geodesic shape. The free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user. Throughout the entire process, no complete struts are operably coupled to other complete struts.

A fourth aspect of the present invention provides method of making a polygonal shape from a pre-made form. The polygonal shape is characterized by having correct dihedral and axial angles for use in constructing a geometric shape. The method provides a plurality of triangular pre-made forms, each pre-made form having a triangular shape, first and second inner edges, an outer edge, and an inner face and an outer face. A length of each inner edge and outer edge are determined by the frequency of the geodesic shape, and diameter of the geodesic shape. The method then comprises assembling the polygonal shape, where the total number of pre-made forms in the polygonal shape is either five or six. There are steps to assembling the polygonal shape. The first step involves operably coupling a first pre-made form, along its uncoupled first inner edge to a first face of a first strut, by a first hinge(s). The second step involves operably coupling a second pre-made form, along its uncoupled second inner edge to a second face of the first strut, by a second hinge(s). The third step involves operably coupling the second pre-made form, along its uncoupled first inner edge to a first face of a second strut, by its first hinge(s). The fourth step involves forming a planar precursor to the desired polygonal shape by sequentially operably coupling inner edges of additional pre-made forms to respective faces of struts already in the structure and sequentially operably coupling additional struts to the additional pre-made forms in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms have not been coupled to respective faces of the last additional strut. The fifth step involves forming the desired polygonal shape by raising the planar precursor and operably coupling the inner edge of a last coupled pre-made form and a second inner edge of the first premade form to respective faces of the last additional strut, resulting in creating correct dihedral angles which are between the inner faces of the premade forms and faces of the coupled struts, and the correct axial angles which are between a z axis of the desired polygonal shape and the inner face of each premade form without any additional measurement. Throughout the entirety of the assembly, no struts are operably coupled to other struts.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Definitions

Hereinafter, unless defined otherwise, the term “pre-made form” is defined as a planar triangular shape having first and second inner edges8,10, an inner face11and an outer face13and an outer edge12, depicted inFIG.1A.

Hereinafter, unless defined otherwise, the term “polygonal shape” is defined as comprising five or six struts6each with a first face operably coupled to a first hinge(s) and second face operably coupled a second hinge(s), and five or six pre-made forms, e.g.14inFIG.1E.

Hereinafter, unless defined otherwise, the term “geodesic” is the shortest distance between two points on a sphere.

Hereinafter, unless defined otherwise, the term “geodesic shape” is defined as comprising a plurality of polygonal shapes14and plurality of polygonal patches222, depicted inFIGS.3A-C.

One objective of the present invention is to provide a method of constructing geodesic domes by using pre-made forms and struts with hinges that are constructed at pre-measured intervals. This allows for easy assembly of a geodesic dome without time and cost-intensive measuring and fitting on site.

With this invention, a full concrete dome can be assembled in a day and a half onsite without recutting or otherwise customizing the struts or the pre-made forms. In particular, ensuring that the struts do not operably couple to other struts and making the pre-made forms the load-bearing sections of the geodesic dome ensures that the struts do not have to be re-measured or recut to fit into place, saving considerable time and the use of additional equipment onsite.

A second objective of the present invention is to provide a methodology allowing for ease of construction of a Geodesic Dome strut-panel system regardless of dome frequency or diameter by achieving the correct axial and dihedral angles associated with geodesic dome construction automatically, effortlessly and as the proximal result of the use of a hinge(s) attaching a strut (be it a 2×4, 6, 8 etc.) lengthwise to each of the three panel edges of each panel, thence attaching struts of like length together from adjacent panels thus allowing a free range of motion of each strut-panel interface of each panel along the panel-edge axis. The strut-to-strut assembly of adjacent panels is necessarily a fixed interface. The motion allowed each strut/panel interface can therefore accommodate differing dihedral angles, one side of the strut-strut interface to the other.

The hinges of the present invention allow for freedom of motion along the interface of each strut and panel, allowing each to accommodate differing dihedral angles. This allows the axial and dihedral angles to be arrived at passively, as an inherent result of the invention's assembly. As the dome is constructed with this invention, the construction will increasingly and effortlessly approximate a sphere as assembly moves towards completion. The invention spontaneously arrives passively at the correct axial and dihedral angles and the strength of the structure increases dramatically as the assembly progresses.

When these dihedral angles are combined with the accompanying axial angles, normally combining the panels into the right angles at the right time during construction is challenging, requiring several measurements and occasional adjusting or cutting. The present invention avoids this difficulty.

As the dome is constructed using this invention, by a singular panel at a time or pre-assembled into groups of pentagons, hexagons or otherwise groupings, construction will increasingly and effortlessly approximate a sphere as the assembly moves toward completion. The present invention spontaneously arrives passively at the correct axial and dihedral angles and the strength of the structure increases dramatically as the assembly progresses.

This result of correct axial and dihedral angles are arrived at by simply allowing freedom of movement along the panel-to-adjacent-strut interface. The interface is not fixed, and uses a hinge to allow movement in the plane of the hinge. Every panel has three struts running along its edges attached by a hinge or series of hinges that allow motion only in the hinge plane.

Simultaneously, the strut-to-strut interface is rigidly fixed, i.e. it is bolted or clamped to the strut of an adjacent panel. In this way, each panel edge with its attached-by-hinge strut is free to approximate the true/ideal axial and dihedral angles that the dome spontaneously approximates as the assembly progresses. This result is achieved without axial or dihedral calculation or component fabrication (other than cutting panels to correct sizes) to achieve the desired result. It is arrived at passively.

A one-eighth polpolmodel was built in an attempt to prove this concept. At no time were the dihedral or axial angles measured in the assembly process. As was claimed above, the construction/assembly process achieved this result for these angles spontaneously and as a consequence of the hinged strut/panel; i.e. by simply rigidly fixing adjacent struts of different panels while flexibly connecting struts to their respective panels in the plane of the hinge joint that allowed for that freedom of movement in that plane.

What is unique about this approach to constructing Geodesic Domes is that if the ‘strut-panel’ interface is allowed to remain flexible along the hinge/strut plane, the proper dome ‘geometry’, i.e. the array of dihedral and axial angles can be arrived at passively. The dome will simply “find” the proper angles as a function of some conservation of stress and energy law of nature that it enjoys. Only one thing is necessary from a material fabrication standpoint: Exact panel lengths. Exact panel lengths achieves the correct ‘radial’ angles such that when the pentagons and hexagons are constructed, ‘closing’ the last strut-strut interface ‘forces’ the dome geometry from 2-d to 3-d; the hinged panel/strut angle is brought out at each panel edge across the entire pentagon or hexagon. At no time then are we nailing or screwing panels to struts or panels to panels.

Initial research in constructing this model showed important considerations. When constructing at this scale, the selection of materials became increasingly flimsy: The 150 panels used were made of a 220″ plywood, and the struts of a very flexible PVC trim product. The strut-strut interfaces were held together with 4″ cable ties. The hinge ended-up being a very tough ordnance tape as even the smallest hinges seemed immensely impractical for the sheer numbers involved (2 hinges per strut, 3 struts per panel, 160 panels per dome, for a total of 960 hinges installed). When the dome was ‘closed’, the flexibility of these components failed to ‘force the geometry’, i.e. it failed to cause the flat, 2-d pentagons/hexagons into 3-d dome geometry. The eventual working solution involved securing the panel/panel interface with cable ties at the end of the panels to maintain the dome geometry. This research showed that the hinge to be used must be rigid in every sense other than the desired direction of motion.

A first aspect of the present invention provides a method of making a geodesic shape2. The method comprises of providing and assembling a plurality of pre-made forms4, and a plurality of struts6, as shown inFIG.1A-F. The pre-made forms have a triangular shape, first and second inner edges8,10, an inner face11and an outer face13and an outer edge12. The length of each inner edge8,10and outer edge12are determined by the frequency of the desired geodesic shape, diameter of the desired geodesic shape, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere.

FIGS.3A-Cdepict side elevation views of stages of construction of a geodesic shape2from a plurality of polygonal shapes14and plurality of polygonal patches222. The geodesic shape2may be a geodesic dome or sphere.FIG.3Adepicts a possible first stage1in the construction of the geodesic shape2.FIG.3Bdepicts a possible intermediate stage3after the possible first stage1in the construction of the geodesic shape2shown inFIG.3A.FIG.3Cdepicts a completed geodesic shape2. The geodesic shape2comprises a plurality of polygonal shapes14and plurality of polygonal patches222. The plurality of polygonal shapes14and plurality of polygonal patches222are made from pre-made forms4, and a plurality of struts6, as shown inFIGS.1A-F.

FIG.1Adepicts a plan view of the pre-made forms4, having a triangular shape, first and second inner edges8,10, an inner face11and an outer face13and an outer edge12. A length of each inner edge8,10and outer edge12are determined by the frequency of the desired geodesic shape2, diameter of the desired geodesic shape2, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere. A desired polygonal shape14is assembled using the pre-made forms4and struts6. A first pre-made form16is operably coupled along its uncoupled first inner edge18to a first face20of a first strut22, by a first hinge(s)24.

FIG.1Bdepicts a plan view ofFIG.1Aafter a second26pre-made form4is operably coupled along its uncoupled second inner edge28to a second face30of the first strut22, by a second hinge(s)32.

FIG.1Cdepicts a plan view ofFIG.1Bafter the second pre-made form26is operably coupled along its uncoupled first inner edge34to a first face36of a second strut38, by its first hinge(s)40.

FIG.1Ddepicts a plan view ofFIG.1Cafter additional pre-made forms4have been operably coupled to respective faces of struts already in the structure and additional struts41have been operably coupled to the additional pre-made forms42in the structure with uncoupled inner edges. This results in a structure in which the inner edges of the first and last pre-made forms have not been coupled to respective faces of the last additional strut47.

FIG.1Edepicts a plan view ofFIG.1Dafter operably coupling the inner edge of a last coupled pre-made form and a second inner edge19of the first premade form to respective faces of the last additional strut, creating a desired dihedral angles θ1, θ2between the inner edges of the pre-made forms, and creating a desired axial angles θ3between a z axis of the desired polygonal shape and the inner face of each premade form, thus forming the desired polygonal shape14. The dihedral angles θ1, θ2may advantageously be the same or different.FIG.1Ealso shows the Z axis51of the desired polygonal shape14, which is a line going through the center of the desired polygonal shape14. The axial angle θ3is between the Z axis51and the inside face11of each of the premade forms.

FIG.1Fdepicts a plan view of a polygonal patch222. The polygonal patch222is formed by operably coupling a seventh pre-made form124, along its uncoupled first inner edge to a first face of a seventh strut126, by a first hinge(s)128, operably coupling an eighth pre-made form130, along its uncoupled second inner edge to a second face133of the seventh strut126, by a second hinge(s), operably coupling the eighth pre-made form, along its uncoupled first inner edge132to a first face136of a eighth strut135, by its first hinge(s)138, and operably coupling a ninth pre-made form140, along its uncoupled second inner edge to a second face142of the eighth strut134, by its second hinge(s)144.

FIG.9depicts a flow diagram of a method198for assembling a desired polygonal shape14using the pre-made forms4and struts6. The desired polygonal shape14is assembled using the method198in several steps. The first step200comprises operably coupling a first pre-made form16, along its uncoupled first inner edge18to a first face20of a first strut22, by a first hinge(s)24. The second step202comprises operably coupling a second26pre-made form4, along its uncoupled second inner edge28to a second face30of the first strut22, by a second hinge(s)32. The third step204comprises operably coupling the second pre-made form26, along its uncoupled first inner edge34to a first face36of a second strut38, by a its first hinge(s)40. The fourth step206comprises sequentially operably coupling inner edges of additional pre-made forms4to respective faces of struts already in the structure and sequentially operably coupling additional struts41to the additional pre-made forms42in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms have not been coupled to respective faces of the last additional strut47. The fifth step208comprises forming the desired polygonal shape14by operably coupling the inner edge of a last coupled pre-made form and a second inner edge19of the first premade form to respective faces of the last additional strut, creating a desired dihedral angles θ1, θ2between the inner edges of the pre-made forms and creating desired axial angles θ3between a z axis of the desired polygonal shape and the inner face of each premade form. The total number of pre-made forms in the polygonal shape14is either five, as shown inFIG.2A-B, or six, as shown inFIG.1E. The resulting desired polygonal shape14and additional desired polygonal shapes14made using the same steps are connected at preset angles in known geodesic form and function, so that the desired polygonal shapes combine to form a desired geodesic shape44, as shown inFIG.1E. Throughout the process, no struts are operably coupled to other struts.

FIG.10depicts a flow diagram listing the steps of a method220for assembling a polygonal patch222, as shown inFIG.1F, and described in associated text, herein. The first step210of the method220involves operably coupling a seventh pre-made form124, along its uncoupled first inner edge to a first face of a seventh strut126, by a first hinge(s)128. A second step212involves operably coupling an eighth pre-made form130, along its uncoupled second inner edge to a second face133of the seventh strut126, by a second hinge(s). A third step214involves operably coupling the eighth pre-made form, along its uncoupled first inner edge132to a first face136of an eighth strut135, by its first hinge(s)138. A fourth step216involves operably coupling a ninth pre-made form140, along its uncoupled second inner edge to a second face142of the eighth strut134, by its second hinge(s)144.

FIG.11depicts a flow chart listing the steps of a method224for assembling a geodesic shape2, as shown inFIG.1E. The method224comprises a first step218, coupling desired polygonal shapes14made using the aforementioned steps to desired polygonal shapes14, premade forms4, and to polygonal patches222made using the aforementioned steps by coupling their outer edges in known geodesic form and function, so that the desired polygonal shapes, polygonal patches, and additional pre-made forms create a desired geodesic shape44.

Throughout the entire method, no struts are operably coupled to other struts. Throughout the entire method, the free range of motion of each strut-panel interface146of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user.

FIG.8depicts a front elevation view of a hexagonal polygonal shape using partial struts226,228. In an embodiment a number of struts are comprised of first partial struts and second partial struts226,228, as shown inFIG.8. The first pre-made form16is operably coupled along its uncoupled first inner edge8to a first partial strut226, by a first hinge(s)24. A second pre-made form26is operably coupled along its uncoupled second inner edge to a second partial strut228, by a second hinge(s)32. The first partial strut226is operably coupled to the second partial strut228, forming a complete strut. No complete struts are operably coupled to other complete struts.

In one embodiment, the hinges23are within two inches of the outside edges of the pre-made forms. In an embodiment, after the desired polygonal shape is created a compression hinge is operably coupled to a common joint of the pre-made forms comprising the polygonal shape14where an axial angle is formed.

In an embodiment, gaps46in the desired geodesic shape44that are not covered by the desired polygonal shapes are covered by additional pre-made forms4shaped to cover the gaps.

FIGS.16A and16Bdepict a cross-sectional view of the interface between two panels4. In an embodiment, all pre-made forms4and all struts6have been cut and shaped before on site construction. In an embodiment, the pre-made forms have beveled edges302, which allow the pre-made forms to come together without gaps in the structure, as shown inFIGS.16A and16B.

FIGS.4A-Cdepict side elevation views of an assembled geodesic shape44with extension doors or windows50, bump out doors or windows52, or rectilinear doors or windows54in accordance with embodiments of the present invention. In an embodiment, the desired geodesic shape is selected from the group consisting of a full sphere, dome, or a partial sphere where individual desired polygonal shapes have been omitted so as to leave space for a doorway or window.

In an embodiment, one or more of the premade forms are transparent56, in order to serve as a window.

In an embodiment, the polygonal shapes omitted to leave space for a doorway or window are used to create extension doors or windows52, bump out doors or windows54or rectilinear bump out doors or windows56.

In an embodiment, the geodesic structure has a frequency of 4.

In an embodiment, the geodesic structure has a diameter of 40 feet, and there are 30 pre-made forms with sides measuring 5′0¾″ by 5′10-⅞″ by 5′0-¾″, 30 pre-made forms measuring 5′10-⅝″ by 5′10-⅞″ by 5′10-⅝″, 60 pre-made forms measuring 5′10-⅝″ by 6′3⅛″ by 5′11-⅚″, 30 pre-made forms measuring 6′3⅛″ by 6′6″ by 6′3⅛″, and 10 pre-made forms measuring 6′6 by 6′6 by 6′6.

In an embodiment, the hinges are utility hinges.

In an embodiment, the desired geodesic shape44is watertight and/or vapor tight.

FIG.5depicts a front elevation view of a polygonal shape with anchors60attached. In an embodiment, anchors60are attached to the desired polygonal shape, and concrete62is poured onto the desired polygonal shape, as shown inFIG.5. Once the concrete has set, a crane lifts the desired polygonal shape into place.

In an embodiment, the desired polygonal shapes are removed after the concrete has set in place.

In an embodiment, the forms4create a desired tile or panel finish that remains on the interior of the concrete dome.

FIG.6depicts a dirt exterior layer66with vegetation68on a desired geodesic shape49. In an embodiment, after the concrete62has set, a watershed insulating blanket64(a waterproof layer) is placed on top of the concrete layer, and an exterior layer66is place on top of the waterproof layer, as shown inFIG.6.

In an embodiment, the exterior layer66is dirt, sod, or turf.

In an embodiment, vegetation68is encouraged to grow on the exterior layer of dirt, sod, or turf, as shown inFIG.6.

FIG.7depicts the hexagonal polygonal shape depicted inFIG.1Ebefore it has been raised, so that the inner edge43of a last coupled pre-made form110and a second inner edge19of the first premade form16are operably coupled to respective faces of the last additional strut, creating a desired dihedral angles θ1, θ2between the inner edges of the pre-made forms, and creating a desired axial angles θ3between a z axis51of the desired polygonal shape and the inner face49of each premade form, thus forming the desired polygonal shape14. A second aspect of the present invention provides an apparatus for making a polygonal shape, as shown inFIG.7. The apparatus is comprised of five or six struts6each with a first face operably coupled to a first hinge(s) and second face operably coupled a second hinge(s), and five or six pre-made forms4which are triangular in shape, with first and second inner edges, an inner face11and an outer face13, and an outer edge. The lengths of each inner edges and the outer edge of the pre-made form are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency to create a geodesic dome. A first pre-made form16is operably coupled along its first inner edge18to the first face20of a first strut22by first hinge(s)24. A second pre-made form26is operably coupled along its second inner edge28to a second face30of the first strut22, by its second hinge(s)32. The second pre-made form26is then operably coupled along its first inner edge34to a first face36of a second strut38, by its first hinge(s)40. A third pre-made form70is then operably coupled along its second inner edge72to the second face74of the second strut38by its second hinge(s)76. The third pre-made form70is operably coupled along its first inner edge78to a first face80of a third strut82, by its first hinge(s)84. A fourth pre-made form86is operably coupled along its second inner edge88to a second face90of the third strut82, by its second hinge(s)92. The fourth pre-made form86is operably coupled along its first inner edge96to a first face98of the fourth strut94, by its first hinge(s)100. A fifth pre-made form102may be operably coupled along its second inner edge104to a second face106of the fourth strut100, by its second hinge(s)108if there is a sixth pre-made form110, as shown inFIG.7. The fifth pre-made form102may be operably coupled along its first inner edge112to a first face114of the fifth strut116, by its first hinge(s)118if there is a sixth strut120. A desired polygonal shape14is formed by operably coupling the inner edge43of a final pre-made form and a second inner edge10of the first premade form to respective faces of the last additional strut, creating desired dihedral angles θ1, θ2between the inner edges of the pre-made forms and creating desired axial angles θ3between a z axis of the desired polygonal shape and the inner face of each premade form. Throughout creation of the desired polygonal shape14, no struts6are operably coupled to other struts. The free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user.

In an embodiment, all pre-made forms4and all struts6have been cut and shaped before on site construction.

In an embodiment, there is a kit for making a desired geodesic shape. The kit is comprised of several of the desired polygonal shapes14acting in concert. along with additional pre-made forms4having shapes determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere, designed to cover gaps46in the desired geodesic shape44that are not covered by the desired polygonal shapes14. The desired polygonal shapes14and the additional pre-made forms4act in concert, and are operably coupled at preset angles in known geodesic form and function, so that the desired polygonal shapes14combine to form a desired geodesic shape44without any changes or modifications to any of the struts6or pre-made forms4. Throughout creation of the desired geodesic shape44, no struts6are operably coupled to other struts.

In an embodiment, wherein the desired geodesic shape44is selected from the group consisting of a full sphere, half sphere, or a partial sphere where individual polygons have been omitted so as to leave space for a doorway or window.

In an embodiment, the hinges are utility hinges.

In an embodiment, the desired geodesic shape44has a frequency of 4 and a 40 foot diameter, so that each polygonal shape14weighs a maximum of 5,000 pounds. In a preferred embodiment, each polygonal shape14weighs a maximum of 4,500 pounds.

In an embodiment, the geodesic structure has a diameter of 40 feet and there are 30 pre-made forms with sides measuring 5′0¾″ by 5′10-⅞″ by 5′0¾″, 30 pre-made forms measuring 5′10-⅝″ by 5′10-⅞″ by 5′10-⅝″, 60 pre-made forms measuring 5′10-⅝″ by 6′3⅛″ by 5′11-⅚″, 30 pre-made forms measuring 6′3⅛″ by 6′6″ by 6′3⅛″, and 10 pre-made forms measuring 6′6 by 6′6 by 6′6.

In an embodiment, the desired geodesic shape is watertight and/or vapor tight.

In an embodiment, anchors60are attached to the desired polygonal shape, concrete62is poured onto the desired polygonal shape, and once the concrete62has set a crane lifts the desired polygonal shape into place.

With a full of set of parts, the full concrete form62can be put up within a day and a half onsite without recutting or otherwise customizing the struts or pre-made forms.

In an embodiment, the pre-made forms create a desired tile or panel finish that remains on the interior of the concrete dome.

In an embodiment, after the concrete has set, a watershed insulating blanket64(a waterproof layer) is placed on top of the concrete layer, and an exterior layer66is placed on top of the waterproof layer64.

In an embodiment, the desired geodesic shape is a frequency4and a 40 foot diameter, so that each polygon weighs a maximum of 5,000 pounds.

In an embodiment, the geodesic structure has a diameter of 40 feet and there are 30 pre-made forms with sides measuring 5′0¾″ by 5′10-⅞″ by 5′0¾″, 30 pre-made forms measuring 5′10-⅝″ by 5′10-⅞″ by 5′10-⅝″, 60 pre-made forms measuring 5′10-⅝″ by 6′3⅛″ by 5′11-⅚″, 30 pre-made forms measuring 6′3⅛″ by 6′6″ by 6′3⅛″, and 10 pre-made forms measuring 6′6 by 6′6 by 6′6.

In an embodiment, the exterior layer66is dirt, sod, or turf. In an embodiment, vegetation68is encouraged to grow on the exterior layer of dirt, sod, or turf.

In an embodiment, a number of struts are comprised of first partial struts226and second partial struts228. A first pre-made form16is operably coupled along its uncoupled first inner edge to a first face of a first partial strut226, by a first hinge(s)234. A second pre-made form26is operably coupled along its uncoupled second inner edge to a second partial strut228, by a second hinge(s). The first partial strut is operably coupled to the second partial strut, forming a complete strut. No complete struts are operably coupled to other complete struts.

FIG.12depicts a flow diagram of a method276of assembling a precursor geodesic shape260depicted inFIG.8and described in associated text, herein. The method276includes steps for assembling a desired geodesic shape2,44from a plurality of triangular pre-made forms having a triangular shape, first and second inner edges, an inner face11and an outer face13, and an outer edge. The length of each inner edge and outer edge are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency when creating a geodesic dome or sphere. The method includes steps278,280,282,284, and286for assembling a polygonal shape. The first step278involves operably coupling a first pre-made form16, along its uncoupled first inner edge to the first face of a first partial strut226, by its first hinge(s)234. The second step280involves sequentially operably coupling inner edges of the first pre-made form to respective faces of partial struts. The third step282involves operably coupling a second pre-made form26, along its uncoupled inner edges to respective faces of second and third partial struts228,240. The fourth step284involves operably coupling the first partial226strut of the first pre-made form to the second partial strut228of the second pre-made form26in a fixed interface236forming a complete strut, thus allowing a free range of motion238of each strut-panel interface of each panel along its axis. The fifth step286involves sequentially operably coupling partial struts operably coupled to inner edges of additional pre-made forms to respective partial struts already in the structure and sequentially operably coupling additional partial struts to the additional pre-made forms in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms16,45have not been coupled. The desired polygonal shape is formed by operably coupling a partial strut258operably coupled to an inner edge of a last coupled pre-made form45and a partial strut256operably coupled to a second inner edge of the first premade form16in a fixed interface forming a complete strut, creating desired dihedral angles between the inner edges of the pre-made forms and creating a desired axial angles θ3between a z axis of the desired polygonal shape and the inner face of each premade form. The total number of pre-made forms in the polygonal shape is either five or six. The method includes steps288for assembling a polygonal patch222, as shown in the flowchart ofFIG.13.

FIG.13depicts a flow chart of a method for assembling a polygonal patch. The first step290involves operably coupling a seventh pre-made form, along its uncoupled first inner edge to a first face of a seventh strut, by a first hinge(s). The second step292involves operably coupling an eighth pre-made form, along its uncoupled second inner edge to a first face of an eighth strut, by a second hinge(s). The third step294involves operably coupling the seventh strut and the eighth strut135. The fourth step296involves operably coupling the eighth pre-made form, along its uncoupled first inner edge to a first face of a ninth strut, by its first hinge(s). The fifth step298involves operably coupling a ninth pre-made form, along its uncoupled second inner edge to a first face of a tenth strut. The sixth step300includes operably coupling the ninth strut and the tenth strut.

FIG.14depicts a flow diagram of a method for assembling a geodesic shape. The method includes steps302for assembling a geodesic shape, as shown inFIG.14. The first step304includes coupling desired polygonal shapes made using the previously described steps to desired polygonal shapes, premade forms, and to polygonal patches made using the previously described steps by coupling their outer edges in known geodesic form and function, so that the desired polygonal shapes, polygonal patches, and additional pre-made forms create a geodesic shape. The free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any additional measurement or cutting by the user. Throughout the entire process, no complete struts are operably coupled to other complete struts.

FIG.8depicts a front elevation view of a hexagonal polygonal shape using partial struts226,228. The apparatus includes ten or twelve partial struts225each with a first face232operably coupled to a first hinge(s)234. The apparatus has five or six pre-made forms4comprised of a triangular shape, first and second inner edges8,10, an inner face11and an outer face13, and an outer edge12. The length of each inner edges and outer edge are determined by the frequency of the geodesic shape, diameter of the geodesic shape, and known formulas for relating diameter and frequency to create a geodesic dome. The apparatus has a first pre-made form16and a first partial strut226. The first pre-made form16is operably coupled along its first inner edge to a first face232of a first partial strut226by a first hinge(s)234. The apparatus has a second pre-made form26. The second pre-made form26is operably coupled along its second inner edge28to a first face232of a second partial strut228, by its first hinge(s)234. The first partial strut226and the second partial strut228are operably coupled in a fixed interface236forming a complete strut, thus allowing a free range of motion238of each strut-panel interface of each panel along its axis. The apparatus includes a third partial strut240. The second pre-made form26is operably coupled along its first inner edge to a first face232of the third partial strut240, by its first hinge(s)234. The apparatus includes a third pre-made form70, where the third pre-made form70is operably coupled along its second inner edge to a first face232of a fourth partial strut242by its first hinge(s)234. The third partial strut240and the fourth partial strut242are operably coupled in a fixed interface236forming a complete strut, thus allowing a free range of motion238of each strut-panel interface of each panel along its axis. The apparatus includes a fifth partial strut244, where the third pre-made form70is operably coupled along its first inner edge to a first face232of the fifth partial strut244, by its first hinge(s)234. The apparatus includes a fourth pre-made form86, where the fourth pre-made form is operably coupled along its second inner edge to a first face232of a sixth partial strut246, by its first hinge(s)234. The fifth partial strut244and the sixth partial strut246are operably coupled in a fixed interface236forming a complete strut, thus allowing a free range of motion of each strut-panel interface of each panel along its axis. The apparatus includes a seventh partial strut248, where the fourth pre-made form86is operably coupled along its first inner edge to a first face of the seventh partial strut, by its first hinge(s). The apparatus includes a fifth pre-made form102, where the fifth pre-made form may be operably coupled along its second inner edge to a first face of the eighth partial strut250, by its second hinge(s) if there is a sixth pre-made form110. The seventh partial strut248and the eighth partial strut250are operably coupled in a fixed interface forming a complete strut, thus allowing a free range of motion of each strut-panel interface of each panel along its axis if there is a sixth pre-made form. The apparatus includes a ninth partial strut252, where the fifth pre-made form102may be operably coupled along its first inner edge to a first face of the ninth partial strut252, by its first hinge(s) if there is a sixth partial strut246. A desired polygonal shape is formed by operably coupling the inner edge of a final pre-made form to the ninth partial strut252and a second inner edge of the first premade form to respective faces of a tenth partial strut254and operably coupling the ninth and tenth partial struts in a fixed interface forming a complete strut, creating desired dihedral angles between the inner edges of the pre-made forms and creating a desired axial angles θ3between a z axis of the desired polygonal shape and the inner face of each premade form. The free range of motion of each strut-panel interface of each panel along its axis aligns itself into the ideal axial and dihedral angles for the desired geodesic shape spontaneously as the assembly progresses, without any measurement or cutting by the user. Throughout the apparatus, no complete struts are operably coupled to other complete struts.

In an embodiment, all pre-made forms4and all partial struts225have been cut and shaped before on site construction.

FIG.15depicts a front view of a panel-to-adjacent strut interface146, taken along the line15-15inFIG.1B, showing the free range of motion238of the desired dihedral angles θ1, θ2between the pre-made forms4and the struts6.

FIG.17depicts a front view of a panel-to-adjacent strut interface146, taken along the line17-17inFIG.8, showing the free range of motion238of the desired dihedral angles θ1, θ2between the pre-made forms26and16and the partial struts228,226.

FIGS.1A-1Edepict the operational stages for making a polygonal shape14from a pre-made form16. The polygonal shape14is characterized by having correct dihedral θ1, θ2and axial angles θ3for use in constructing a geodesic shape2. In the method220a plurality of triangular pre-made forms are provided, each pre-made form having a triangular shape, first and second inner edges8,10, an outer edge12, and an inner face11and an outer face13. A length of each inner edge8,10and outer edge12is determined by the frequency of the geodesic shape2, and diameter of the geodesic shape2. The method220then comprises assembling the polygonal shape14, where the total number of pre-made forms in the polygonal shape is either five or six. There are steps210,212,214and216to assembling the polygonal shape14. In the step220, a first pre-made form16is operably coupled along its uncoupled first inner edge18to a first face20of a first strut22, by a first hinge(s)24. In step212a second pre-made form26is operably coupled along its uncoupled second inner edge28to a second face30of the first strut22, by a second hinge(s)32. In a step214, the second pre-made form26is operably coupled along its uncoupled first inner edge34to a first face36of a second strut38, by its first hinge(s)40. In a step216a planar precursor260of the desired polygonal shape14is formed by sequentially operably coupling inner edges of additional pre-made forms to respective faces of struts already in the structure and sequentially operably coupling additional struts to the additional pre-made forms in the structure with uncoupled inner edges, resulting in a structure in which the inner edges of the first and last pre-made forms have not been coupled to respective faces of the last additional strut. In a concluding step, the desired polygonal shape14may be formed by raising the planar precursor260and operably coupling the inner edge of a last coupled pre-made form and a second inner edge of the first premade form to respective faces of the last additional strut, resulting in creating correct dihedral angles θ1, θ2which are between the inner faces256of the premade forms4and faces258of the coupled struts6and the correct axial angles θ3which are between a z axis of the desired polygonal shape and the inner face256of each premade form4without any additional measurement. Throughout the entirety of the assembly, no struts are operably coupled to other struts.

FIG.1Fdepicts the operational stages for making a desired geodesic shape44from the polygonal shape. First a polygonal patch222is assembled. The first step of assembling a polygonal patch222involves operably coupling a seventh pre-made form124, along its uncoupled first inner edge to a first face of a seventh strut126, by a first hinge(s)128. The second step involves operably coupling an eighth pre-made form130, along its uncoupled second inner edge to a second face133of the seventh strut126, by a second hinge(s). The third step involves operably coupling the eighth pre-made form130, along its uncoupled first inner edge132to a first face136of an eighth strut135, by its first hinge(s)138. The fourth step involves operably coupling a ninth pre-made form140, along its uncoupled second inner edge to a second face142of the eighth strut134, by its second hinge(s)144. A geodesic shape is thus assembled by coupling desired polygonal shapes made using the previously described steps to desired polygonal shapes, pre-made forms, and to polygonal patches made using the previously described steps by coupling their outer edges, so that the desired polygonal shapes, polygonal patches and additional pre-made forms create a geodesic shape. Throughout the assembly of the geodesic shape, no struts are operably coupled to other struts.

In one embodiment, a number of struts are comprised of first partial struts and second partial struts. A first pre-made form16is operably coupled along its uncoupled first inner edge to a first partial strut226, by a first hinge(s)234. A second pre-made form26is operably coupled along its uncoupled second inner edge to a second partial strut228, by a second hinge(s). The first partial strut is operably coupled to the second partial strut, forming a complete strut. Throughout the assembly, no complete struts are operably coupled to other complete struts.

In one embodiment, the hinges are within two inches of the outside edges of the pre-made forms.

In one embodiment, after the desired polygonal shape is created a compression hinge is operably coupled to a common joint of the pre-made forms comprising the polygonal shape where an axial angle is formed.

In one embodiment, all pre-made forms and all struts have been cut and shaped before on site construction.

In one embodiment, the desired geodesic shape is selected from the group consisting of a full sphere, dome, or a partial sphere where individual desired polygonal shapes have been omitted so as to leave space for a doorway or window.

In one embodiment, one or more of the premade forms are transparent, in order to serve as a window.

In one embodiment, the polygonal shapes omitted to leave space for a doorway or window are used to create extension doors or windows, bump out doors or windows or rectilinear bump out doors or windows.

In one embodiment, the geodesic structure has a frequency of 4.

In one embodiment, the geodesic structure has a diameter of 40 feet;

In one embodiment, there are 30 pre-made forms with sides measuring 5′0¾″ by 5′10-⅞″ by 5′0¾″, 30 pre-made forms measuring 5′10-⅝″ by 5′10-⅞″ by 5′10-⅝″, 60 pre-made forms measuring 5′10-⅝″ by 6′3⅛″ by 5′11-⅚″, 30 pre-made forms measuring 6′3⅛″ by 6′6″ by 6′3⅛″, and 10 pre-made forms measuring 6′6 by 6′6 by 6′6.

In one embodiment, the hinges are utility hinges.

In one embodiment, the desired geodesic shape is watertight and/or vapor tight.

In one embodiment, anchors are attached to each desired polygonal shape, concrete is poured onto the desired polygonal shape, and once the concrete has set a crane lifts the desired polygonal shape by the anchors into place on a foundation upon which the geodesic shape rests.

In one embodiment, the desired polygonal shapes are removed after the concrete has set in place.

In one embodiment, the pre-made forms create a desired tile or panel finish that remains on the interior of the concrete dome.

In one embodiment, after the concrete has set and the geodesic shape has been created, a watershed insulating blanket is placed on top of the concrete layer, and an exterior layer is placed on top of the waterproof layer.

In one embodiment, the exterior layer is dirt, sod, or turf.

In one embodiment, vegetation is encouraged to grow on the exterior layer of dirt, sod, or turf.