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[0001]    This application is a continuation-in-part of U.S. application Ser. No. 11/879,582, filed on Jul. 18, 2007, now allowed. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates generally to geodesic domes, and more specifically to a prefabricated plastic tile and a strut designed for use together to create a strong, yet easy-to-assemble, geodesic dome. 
         [0004]    2. Background of the Invention 
         [0005]    Structures in the form of geodesic domes have been being built since their invention by Buckminster Fuller in the 1950&#39;s, however their construction, until now, has involved a complicated and difficult procedure. A geodesic dome comprises a configuration of repeating geometric shapes, such as triangles, which form the dome&#39;s surface. The architecture of the dome structure is typically a series of struts which link to hubs to create the dome&#39;s framework. The area, or space, created between any three contiguous struts, i.e. the area of the triangles formed by these repeated struts and hubs, must necessarily be sub-divided, enclosed, and covered, as they are of a sizable dimension which is interdependent with the diameter of the dome itself. 
         [0006]    In some prior art domes, a plurality of geometric tiles are secured together to form a three-dimensional geometric shape, which is assembled with other such secured-together three-dimensional geometric shapes in order to form the dome. This method of assembly is arduous and inefficient. 
         [0007]    One prior art method of constructing geodesic domes involves manipulating polygonal panels of the dome so that they slide into lateral pockets formed on each side of a generally I-beam shaped strut. Such manipulation may not be difficult when inserting a first side of the panel, but once a first side is locked into place, it appears impractical, if not impossible, to angle and manipulate subsequent sides of the panel into place within the pockets of other struts. 
         [0008]    Some prior art panels for geodesic domes are manufactured in layers, with inner and outer faces secured to intermediate support structure. Such a manufacturing method is more complicated and costly than desired. 
         [0009]    In some prior art domes, in order to finish the interior of the dome after assembling the outer structure, panels of sheetrock or some other finishing material must be individually and precisely cut to fit the unique shape of each geometric section of the dome, and then taped and painted. This is a very time consuming and difficult process. 
         [0010]    Prior art geodesic domes are manufactured by a process that involves many steps, and includes a complex structure to attach adjacent tiles to the struts that support them. The tiles of the prior art are not designed for, nor capable of, supporting significant amounts of weight, as would be necessary if the dome is to be earth-sheltered. 
         [0011]    It is known that earth-sheltering a structure provides advantages in the energy needs for heating and cooling that structure. In order to be earth-sheltered, a structure must be capable of supporting the significant weight of the dirt located above the structure. Prior art panels and systems for building geodesic domes are not designed to bear such heavy loads. 
         [0012]    There is a need in the art for a strong, lightweight preformed, easy-to-manufacture tile designed to support a significant amount of weight. There is a need for the tile and the struts which support it to be capable of being assembled to form a geodesic dome quickly and easily, with a minimal amount of skill and tools required. In addition, the tile should either be provided with an interior surface that is manufactured as a finished surface, or have a system that enables a finished surface to be quickly and easily attached thereto. 
       SUMMARY OF THE INVENTION 
       [0013]    The present invention sets forth a tile for use in building a geodesic dome. The tile is a preformed plastic panel having a polygonal, typically triangular, footprint. 
         [0014]    In a first embodiment of the tile, the superior surface of the panel has a non-planar, three-dimensional surface, formed with planar surfaces extending up at an angle from respective side walls of the panel until they meet at a high point at the geometric center of the panel. The inferior surface of the panel includes a stepped recessed portion extending along at least a portion of each side edge of the panel at the juncture of an inferior surface of the side wall and an exterior surface of the side wall. 
         [0015]    The panel may also include any combination of a variety of additional features, including beveled side edges, internally located molded reinforcing ribs for increased strength, an embedded reinforcing member of steel or some other suitable material, a flange extending outwardly from the upper surface of the panel at each of its side edges, and cut-away portions where each of two adjacent sides of the panel meet to accommodate a hub that joins supporting struts of the geodesic dome. Further, the underside of the panel may either comprise a finished interior surface, molded integrally with the rest of the tile, or the underside could comprise a separate sheet of finishing material sized and shaped to cover the exposed molded reinforcing ribs and including connecting structure on the separate sheet of finishing material and on the underside of the rest of the panel, whereby the separate sheet can snap into place on the underside of the panel to quickly and easily provide a finished interior surface of the dome. 
         [0016]    In a second embodiment of the tile, intended for use in a dome that, once completed, has cement sprayed on its exterior surface to improve its ability to support the load of the earth that will be used to bury the dome, the superior surface of the panel has a non-planar, three-dimensional surface, formed with trapezoidal planar surfaces extending up at an angle from a lower end of respective side walls of the panel, with the long edge of each trapezoid being joined to a lower, interior edge of a respective side wall and the short sides of the trapezoids being connected by a small planar top segment having an identical, but smaller, shape to the overall shape of the tile. The angled sides of each of the trapezoidal surfaces are joined to the angled sides of each adjacent trapezoidal surface. The superior surface of the panel has a plurality of ribs thereon, the ribs either being of uniform height or tapering from a larger thickness at the point where the superior surface meets the side walls to a smaller thickness at the highest point of the superior surface. The ribs may either cover the planar top segment, or the planar top segment may be free of ribs. The inferior surface of each of the side walls of the panel includes a stepped recess formed at the juncture of an exterior surface of the side wall and the inferior surface of the side wall, the stepped recess extending along at least a portion of each side edge of the panel. The inferior surface of the panel may be a closed in solid that is planar, or the inferior surface may recessed in a shape that mirrors the superior surface, but without the ribs, thereby increasing the volume of the completed dome&#39;s interior. 
         [0017]    The second embodiment of the panel may also include any combination of a variety of additional features, including beveled side edges and cut-away portions where each of two adjacent sides of the panel meet to accommodate a hub that joins supporting struts of the geodesic dome. 
         [0018]    The present invention further sets forth a strut for use with the inventive tile. A first configuration of the strut has a cross-section in the shape of an I-beam, with an L-shaped bracket seated upon a portion of the length of the lower lateral member of the “I”, such that one leg of the bracket rests along the vertical central member of the “I”, and the other leg of the bracket rests along and extends beyond the lower lateral member of the “I”. A second configuration of the strut has a cross-section substantially in the shape of an inverted “T”, with the two lateral legs of the “T” forming an obtuse angle with the longer, vertical leg of the “T”. 
         [0019]    In use, once the framework for a geodesic dome is built, by connecting together a series of the inventive struts using a plurality of hubs which support the struts at their respective free ends to thereby create polygonal openings bound by a plurality of struts and hubs, the size and shape of the polygonal openings corresponding to the size and shape of the inventive tiles, the tiles of the invention are dropped into respective openings in the framework and secured thereto. 
         [0020]    It is therefore an object of the invention to provide a tile for use in building a geodesic dome, wherein the tile is easy to manufacture and light weight, yet strong enough to support substantial loads. 
         [0021]    It is another object of the invention to provide a tile for use in building a geodesic dome, wherein the tile includes ribs on its superior surface to provide support and a means of retention for a cement shell to be sprayed on the completed dome. 
         [0022]    It is another object of the invention to provide a strut which can, when linked together with additional struts, provide a bound opening designed to easily receive and securely support a tile of the invention thereon. 
         [0023]    It is a further object of the invention to provide a strut and tile system, wherein once the struts are assembled to form a dome structure, the tiles can quickly and easily be dropped into openings bound by the assembled struts, and be secured to the struts. 
         [0024]    These and other objects of the present invention will become readily apparent upon further review of the following specification and drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0025]    Various other objects, features, and attendant advantages of the present invention will become more fully appreciated as the same becomes better understood when considered in conjunction with the accompanying drawings, in which like reference characters designate the same or similar parts throughout the several views, and wherein: 
           [0026]      FIG. 1  is a top view of a first embodiment of the tile of the invention. 
           [0027]      FIG. 2  is a cross-sectional side view of the tile of  FIG. 1  in combination with a first embodiment of the strut of the invention. 
           [0028]      FIG. 3  is a bottom view of the tile of  FIG. 1 . 
           [0029]      FIG. 3A  is a top view of a separate sheet of finishing material for attachment to the underside of the tile of  FIG. 1 . 
           [0030]      FIG. 4  is a side view of the tile of  FIG. 1 . 
           [0031]      FIG. 5  is a top view of a variation of the first embodiment of the tile of the invention. 
           [0032]      FIG. 6  is a side view of the tile of  FIG. 5  in combination with a second embodiment of the strut of the invention. 
           [0033]      FIG. 7  is a cross-sectional side view of the strut of  FIG. 6 . 
           [0034]      FIG. 8  is a cross-sectional view from below of the tile of  FIG. 6 . 
           [0035]      FIG. 9  is a bottom view of the tile of  FIG. 6 . 
           [0036]      FIG. 10  is a cross-sectional side view of a portion of two of the tiles of  FIG. 6  in combination with the strut of  FIG. 6 , as well as a sealing strip. 
           [0037]      FIG. 11  is a top view of one variation of a second embodiment of the tile. 
           [0038]      FIG. 12  is a bottom view of another variation of the second embodiment of the tile. 
           [0039]      FIG. 13  is a cross-sectional view illustrating one variation of the inferior surface and one variation of the ribs on the second embodiment of the tile. 
           [0040]      FIG. 14  is a cross-sectional view illustrating another variation of the inferior surface and another variation of the ribs on the second embodiment of the tile. 
           [0041]      FIG. 15  is a side view of the second embodiment of the tile. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0042]      FIGS. 1 to 4  depict a first embodiment of the tile and strut construction system of the invention.  FIG. 1  shows a top view of a tile  100  of the first embodiment. As viewed from above, the tile  100  is substantially triangular in shape, with three side edges  102 . Where each of the points of the triangle of the tile  100  would be, a small section is cut away leaving a curved free edge  104  whose purpose is to accommodate, during assembly of a geodesic dome, a rounded hub (not shown) that receives and supports a free end of the struts  200  which will serve to support and constrain the tile  100  of the invention when it is used to build a geodesic dome, as discussed further below. The upper surface of the tile  100  is three-dimensional, formed by three substantially triangular portions  106 , with each portion having a lower, base side formed by a respective side edge  102  of the tile  100 , the triangular portions  106  each being angled upward until the upper corners meet together at a point  108  located at the center of the tile  100 , as viewed from above, giving the upper surface of the tile  100  the appearance of a three-faceted diamond. Because the tile and strut construction system is intended to build a geodesic dome that is earth-sheltered, this faceted shape of the upper surface of the tile  100  is important because it serves to deflect the weight of earth resting upon the tiles  100  away from the less supported center  108  of each tile  100  and towards the side edges  102  thereof, where the tile  100  is supported by struts  200 . While the tile  100  is being discussed in terms of a triangular shape, it is understood that the tile can be formed in any suitable polygonal shape. 
         [0043]      FIG. 2  shows a cross-sectional side view of a portion of the tile  100  of the invention in combination with a strut  200  of the invention. The tile  100  can be seen to include triangular portion  106  forming the superior surface of the tile  100 , with a flange  110  extending beyond the side edge  102  of the tile  100  at the superior surface of the tile  100 . Cut into the corner where the lowest point of the side edge  102  and the inferior surface  112  of the tile  100  meet is a stepped recess  114  that extends along a portion of the length of the side edge  102 . The lower portion of each side edge  102  includes such a recess  114 , whose purpose will be discussed shortly. 
         [0044]    The strut  200  shown in  FIG. 2  can be seen to include an I-beam having a vertical central member  202 , an upper lateral member  204  and a lower lateral member  206 . The upper and lower lateral members  204 ,  206  serve as nailers, meaning that they are capable of receiving fasteners therein. If they are not made of a material, such as wood or plastic, that is soft enough to be nailed or screwed into directly, then the lateral members could have predrilled holes located at intervals along their length. This enables tile  100  which is supported by strut  200  to be securely attached thereto by means of a fastener. Strut  200  further includes an L-bracket  208  having a first leg  210  that extends along vertical central member  202  of the I-beam, and a second leg  212  that rests upon and extends beyond lower lateral member  206  of the I-beam. The L-bracket is made of a strong material, such as metal or a very strong plastic, which is capable of supporting significant weight thereon. In use, once a series of struts  200  and hubs (not shown) are assembled to provide the framework for a geodesic dome, with adjacent struts  200  and hubs together forming a substantially triangular opening, the tile  100  of the invention is dropped down within the opening. The recesses  114  on each of the edges  102  of the lower surface  112  of the tile  100  receive the L-bracket  208  of the strut, whereby the L-brackets  208  support the weight of the tile  100 , and each of the flanges  110  extending from the upper surface beyond side edges  102  of the tile  100  extend over and seal against the top of upper lateral member  204  of their respective struts  200 . The inferior surface  112  of tile  100  can be seen to extend below a lower surface of second leg  212  of L-bracket  208 , but not so far down as to be flush with the lower surface of lower lateral member  206  of strut  200 . This allows for a separate finishing sheet to be attached thereto, as will be discussed further below. 
         [0045]    As seen in  FIG. 3 , a series of reinforcement ribs  116  can be molded in unitary fashion into the cavity formed by triangular portions  106  and side edges  102  of the tile  100 . These ribs  116  add strength to the tile  100  while minimizing its weight. The size, number, shape, and arrangement of the ribs  116  shown in the drawings are to be considered merely illustrative. Any size, number, shape, and arrangement of the ribs determined to be desirable are considered to be within the scope of the invention. To further enhance the strength of the tile  100 , the tile  100  may optionally be reinforced by the inclusion of elements of a stronger material, such as by the inclusion of steel re-bars  105 , as seen in phantom in  FIG. 1 . 
         [0046]    It is desirable for the interior surface of the dome to be a smooth, finished surface that is aesthetically pleasing. As seen in  FIG. 3A , a separate sheet of finishing material  120  sized and shaped to cover the underside of the tile  100  is provided with a plurality of first structural elements  122  located on a superior surface thereof. These first structural elements  122  are designed to mate with corresponding second structural elements  118  positioned in corresponding locations on the underside of tile  100 , whereby positioning of separate sheet  120  against the underside of tile  100  such that first structural elements  122  mate with second structural elements  118  causes separate sheet  120  to quickly and easily be secured to the underside of the tile  100 , thereby providing an aesthetically pleasing finished interior on the dome. It is understood that the number and location of structural elements  118 ,  122  shown in the drawing are merely illustrative in nature, and that any suitable number and location of such structural elements is considered to be within the scope of the invention. Similarly, any type of mating structural elements  118 ,  122  that will enable the separate sheet of finishing material  120  to be securely fastened to the underside of tile  100  is considered to be within the scope of the invention. 
         [0047]    If a builder prefers to provide some other form of finished surface, they need merely forego use of the separate sheet of finishing material  120  and attach whatever other form of finishing is desired, such as drywall or paneling, to the underside of the tile  100 . This is not difficult to do because the tile  100  of the invention may be screwed or nailed into. 
         [0048]    In use, a framework for a geodesic dome will be constructed by taking a plurality of the struts  200  of the invention and supporting them at their free ends using hubs (not shown), with each hub typically supporting  4 ,  5 , or  6  struts  200 , whereby the struts and hubs together form a series of substantially triangular openings all over the framework of the dome. A tile  100  of the invention is dropped into each of the substantially triangular openings with the flanges  110  of each tile  100  sealing to an upper surface of the adjacent struts  200  and the weight of each tile  100  being supported by the L-brackets  208  on the adjacent struts  200 . Each tile  100  is then secured to its adjacent struts  200  using a plurality of fasteners, such as nails or screws, through the lateral members of the struts  200 . The interior surface of the dome will be finished, either by securing the separate sheet of finishing material  120  to the underside of the tile  100  using the structural elements  118 ,  122  provided, or by securing an alternative finishing material to the underside of each tile using an alternative means of fastening, such as screws. 
         [0049]    A variation of the first embodiment of the tile and strut construction system of the invention is seen in  FIGS. 5 to 10 .  FIG. 5  shows a top view of a tile  300  of the second embodiment of the invention. As viewed from above, the tile  300  is substantially triangular in shape, with three side edges  302 . Where each of the points of the triangle of the tile  300  would be, a small section is cut away leaving a curved free edge  304  whose purpose is to accommodate, during assembly of a geodesic dome, a rounded hub (not shown) that receives a free end of the struts  400  which will serve to support and constrain the tile  300  of the invention when it is used to build a geodesic dome, as discussed further below. The upper surface of the tile is three-dimensional, formed by three substantially triangular portions  306 , with each portion having a lower, base side formed by a respective side edge  302  of the tile  300 , the triangular portions  306  each being angled upward until the upper corners meet together at a point  308  located at the center of the tile  300 , as viewed from above, giving the upper surface of the tile  300  the appearance of a three-faceted diamond. While the tile  300  is being discussed in terms of a triangular shape, it is understood that the tile can be formed in any suitable polygonal shape. 
         [0050]      FIG. 6  shows a side view of the tile  300  of the invention in combination with two struts  400  of the invention. The tile  300  can be seen to include triangular portion  306  forming the superior surface of the tile  300 . Cut into the corner where the lowest point of the side edge  302  and the inferior surface  312  of the tile  300  meet is a stepped recess  314  that extends along the full length of the side edge  302 . The lower portion of each side edge  302  includes such a recess  314 , whose purpose will be discussed shortly. The side edges  302  of tile  300  can be seen to be beveled  303 , being wider at the top than at the bottom. This beveling facilitates the mating of the tiles  300  with adjacent struts  400  at the appropriate angle necessary for formation of the dome. 
         [0051]      FIG. 7  shows a side edge view of strut  400 , whose cross-section is substantially in the shape of an inverted “T”, with two lateral legs  404  each forming an obtuse angle with the longer, vertical leg  402  of the “T”, the obtuse angle typically being less than 100 degrees. While each of the lateral legs  404  is shown in this Figure to form identical obtuse angles with vertical leg  402 , this is not necessarily the case. It is possible that each of the lateral legs  404  in strut  400  form a different obtuse angle with vertical leg  402  from the obtuse angle formed by the other lateral leg  404 . As seen in  FIG. 6 , each of the recesses  314  of the tile  300  receives one of the lateral legs  404  of an adjacent strut  400 , whereby the inferior surface  312  of tile  300  extends down below the recess  314  to be flush with a lower surface of lateral leg  404  of strut  400 . The strut  400  of this embodiment would be made of any suitable material that is strong enough to support tiles  300  thereon, including, but not limited to steel. Additionally, because the tile  300  to be used with strut  400  is molded of plastic, it is possible, rather than having the lateral legs  404  form an obtuse angle with vertical leg  402 , to have lateral legs  404  made to form a right angle with vertical leg  402 , with tile  300  formed to compensate by changing the angle of the bevel  303  and the recess  314 . 
         [0052]    As seen in  FIG. 8 , a series of reinforcement ribs  316  can be molded in unitary fashion into the cavity formed by triangular portions  306  and side edges  302  of the tile  300 . These ribs add strength to the tile while minimizing its weight. The size, number, shape, and arrangement of the ribs shown in the drawings are to be considered merely illustrative. Any size, number, shape, and arrangement of the ribs determined to be desirable are considered to be within the scope of the invention. To further enhance the strength of the tile  300 , the tile  300  may optionally be reinforced by the inclusion of elements of a stronger material, such as by the inclusion of steel re-bars  305 , as seen in phantom in  FIG. 5 . 
         [0053]      FIG. 9  shows a bottom view of the tile  300 . It can be seen that this embodiment may be manufactured to include a molded, unitary solid lower finished surface  318  which would be flush with a lower surface of lateral legs  404  of the struts  400  supporting it, whereby upon assembly of the tiles  300  to the struts  400  to form a dome (not shown), the interior surface of the dome would have a smooth, finished surface, eliminating the need to cut and fashion sheetrock or some other finishing material to each of the individual panels of the completed dome. In the alternative, as is done in the first embodiment, the lower surface  318  may be manufactured in the form of a separate sheet of finishing material sized and shaped to mate with the underside of tile  300 , the separate sheet of finishing material including structural elements that cooperate with mating structural elements on the underside of tile  300  to allow the separate sheet of finishing material to quickly and easily attach to the underside of the tile  300 , preferably by snapping into place thereon. 
         [0054]      FIG. 10  shows a cross-sectional side view of strut  400  with two tiles  300  supported thereby. Because the tile  300  of the second embodiment does not have an upper flange to form a seal with the adjacent strut  400  (as the tile  100  of the first embodiment does), after assembly of the tiles  300  on opposing sides of a strut  400 , a sealing strip  500 , typically made of plastic, would be placed over the seams of the tiles  300  and the strut  400 . The sealing strip  500  could attach to the tiles  300  themselves, and/or to the exposed end of vertical leg  402  of strut  400 . 
         [0055]    In use, a framework for a geodesic dome will be constructed by taking a plurality of the struts  400  of the invention and supporting them at their free ends using hubs (not shown), with each hub typically supporting  4 ,  5 , or  6  struts  400 , whereby the struts and hubs together form a series of substantially triangular openings all over the framework of the dome. A tile  300  of the invention is dropped into each of the substantially triangular openings with each lateral leg  404  of each strut  400  being received within a respective recess  314  of the tile, with the weight of each tile  300  being supported by the lateral legs  404  of the adjacent struts  400 . Each tile  300  is then secured to its adjacent struts  400  using a plurality of fasteners, such as nails or screws, through the lateral members of the struts  400 . If the tile  300  includes an integrally molded smooth finishing surface on its underside, then no further finishing work need be done. If the tile  300  does not include an integrally molded smooth finishing surface on its underside, then the interior surface of the dome will be finished, either by securing the separate sheet of finishing material to the underside of the tile  100  using mating structural elements provided, or by securing an alternative finishing material to the underside of each tile using an alternative means of fastening, such as screws. 
         [0056]      FIG. 11  shows a top view of a first variation  400  of a second embodiment of the tile of the invention. The tile, overall, has a substantially triangular shape as defined by the three side walls  402 , though it should be understood that this shape of the tile is merely illustrative, and that the tile can have any suitable polygonal shape. Three trapezoidal planar surfaces  406  extend upwardly (above the plane of the paper, toward the viewer) from a lower end of an interior side of a respective one of said side walls  402 , with the longer parallel edge of each trapezoidal planar surface  406  abutting the interior side of its respective side wall  402  and the shorter parallel edges of the three trapezoidal planar surfaces  406  being joined together by a planar top segment  408  having a similar shape to the overall shape of the tile  400 , in this case being triangular. The longer parallel edge of each trapezoidal planar surface  406  is shorter in length than the length of the respective side wall  402  that it abuts. The gap bound by trapezoidal planar surfaces  406  and the portion of the side walls  402  that extend beyond the longer parallel edge of the adjacent trapezoidal planar surfaces  406  is filled by two planar, substantially triangular panels  412  and  414 . Panel  414  is located in the same plane as the inferior surface of the side wall  402 , whereas panel  412  extends upwardly from where its lower edge abuts the edge of panel  414  to where its upper point meets a corner of the triangular planar top segment  408 . It can be seen that where each of the points of the triangle of tile  400  would be, a small section is cut away leaving a curved free edge  404 , similar to curved free edge  104  of the first embodiment of the tile, and serving the same purpose. While the superior surface of tile  400  supports a plurality of ribs, these ribs have been omitted from  FIG. 11  to make it easier to see the other features of the tile. 
         [0057]      FIG. 12  show a bottom view of a second variation  500  of the second embodiment of the tile of the invention. This variation  500  is similar to the first variation  400  in that it has an overall triangular shape defined by side walls  502 , with curved free edges  504  where the points of the triangle would be. Tile  500  includes three trapezoidal planar surfaces  506  extending upwardly (which in this view means below the plane of the paper, away from the viewer) from a lower end of an interior surface of respective side walls  502 , with the upper edges of each trapezoidal planar surface  506  being joined by a triangular planar top segment  508 . The main difference between tile  400  and tile  500  is that in tile  500  the longer parallel edge of each trapezoidal planar surface  506  is equal in length to the length of the respective side wall  502  that it abuts, leaving no gaps that need to be filled. As can be seen in  FIG. 12 , a stepped recess  514  is formed at the juncture of the inferior surface and the exterior side of the side wall  502 , the recess  514  extending along the length of the side wall and serving the purpose of allowing the tile to seat down within the struts used to form the framework of the dome, in a similar fashion to what is shown in  FIGS. 2 ,  6 , and  10 . 
         [0058]      FIG. 13  is a cross-sectional view of tile  400  as seen from line A-A of  FIG. 11 . As can be seen in this view, tile  400  also includes a stepped recess  414  formed at the juncture of the inferior surface and the exterior side of side wall  402 . This figure also illustrates ribs  418  that were omitted from the view shown in  FIG. 11 . It can be seen that the ribs are shown as being of uniform height, and that they cover, not only the superior surfaces of trapezoidal planar surfaces  406 , but also the superior surface of triangular planar top segment  408 . It is understood that an acceptable alternative would be for the ribs to be tapered or for the ribs to cover only the trapezoidal planar surfaces  406 , with planar top segment  408  having no ribs thereon. 
         [0059]      FIG. 14  is a cross-sectional view of tile  500  as seen from line B-B of  FIG. 11 . This figure illustrates the variation where the ribs  520  are tapered from a greater height where the trapezoidal planar surface  506  meets side wall  502  to a smaller height where the trapezoidal planar surface  506  meets planar top segment  508 . It can also be seen that in this figure the planar top segment has no ribs thereon. 
         [0060]      FIG. 15  shows a side view of tile  500 , including an example of how the ribs  522  cover the surface of trapezoidal planar surfaces  506  as well as planar top surface  508 . The size, number, shape, and arrangement of the ribs shown in the drawings are to be considered merely illustrative. Any size, number, shape, and arrangement of the ribs determined to be desirable are considered to be within the scope of the invention. 
         [0061]    In use, the second embodiment of the inventive tile is used to construct a dome in the same manner as is described above with respect to tile  300  and strut  400 . Once construction of the dome has been completed, it is possible to spray a shell of concrete onto the exterior surface of the dome, with support and adherence of the cement onto the dome being supported by the presence of the ribs on the superior surfaces of the tiles. Concrete, being a material that is capable of supporting very large loads in compression, enhances the ability of the dome to support the significant weight of the earth that will ultimately be sheltering the dome.ff. 
         [0062]    It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.

Summary:
The present invention sets forth a tile and strut construction system for a geodesic dome. The tile has a generally triangular shape, with the corners cut out to accommodate hubs which retain supporting struts in position. The tile has a faceted 3-dimensional upper surface, integrally molded reinforcing ribs, and a recess in the lower surface at each of its 3 edges.