Abstract:
One piece, injection-moldable, functionally polyhedral construction modules. The construction modules are thin-walled, cored out versions of a polyhedron. Each construction module comprises one polyhedron wall portion that is interiorly tangent to each face of at least one set of identical faces of a superimposed polyhedron template. Each polyhedron wall portion forms a complex with its tangent face of its superimposed polyhedron template that is the mirror image of at least half of such complexes. Each polyhedron wall portion is visible in both directions along a predetermined axis. Each polyhedron wall portion comprises an asymmetric aligning means that may include one or more snap-fit connectors. Every polyhedron wall portion is part of a single piece of material. Accordingly, these construction modules may be injection molded as single pieces of material, and, when they are aligned face-to-face, they exhibit the constructive properties of their polyhedron templates.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of provisional patent application Ser. No. 60/837,058, filed 2006 Aug. 12 by the present inventor. 
     This is a continuation of application Ser. No. 11/837,518, filed Aug. 12, 2007, now abandoned. 
    
    
     FEDERALLY SPONSORED RESEARCH 
     Not Applicable 
     SEQUENCE LISTING OR PROGRAM 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to construction modules, specifically to releasably connectable modules that exhibit the construction properties of polyhedra and can be easily injection molded as single pieces of plastic. 
     2. Prior Art 
     “Box Shaped” Construction Modules 
     Many space-filling cube and brick-shaped polyhedral modules are known in the prior art. The major advantage of these modules is that they can be molded as one piece of plastic and are, therefore, economical to manufacture. However, these brick-type construction blocks are typically severely limited in terms of which of their six faces can mate with one of the six faces of another, identical, block. Four of their “side” walls are usually sheer, while their top and bottom surfaces incorporate either studs or recesses (as shown in Christiansen&#39;s U.S. Pat. No. 3,005,282—Oct. 24, 1961). In most cases, out of six possible faces of such a brick, there is only one other compatible brick face that can mate with any given mating surface. 
     Having a limited number of compatible mating surfaces on each module is disadvantageous for at least two reasons. First, it complicates construction; the “next block” cannot simply be added on in any direction. Second, it limits accessories that might be added to a structure. For example, if one wanted to attach a snap-on eye, arm, or nose, there are a very limited number of available surfaces for such attachments. 
     There are examples of one-piece brick-type construction modules that are improved in terms of their connecting versatility. In U.S. Pat. No. 6,648,715 (Nov. 18, 2003), Wiens, et al. describe bricks with two single-sex faces that can be mated to one another and four hermaphroditic faces that can be mated to one another. These bricks can be manufactured with relative ease, and they allow any face of a block to mate with at least one other face of an identical block, but they do not allow any face of a block to mate with any other face of an identical block. Tops can be mated to bottoms, and sides can be mated to sides; but tops cannot be mated to tops, sides cannot be mated to tops, sides cannot be mated to bottoms, and bottoms cannot be mated to bottoms. 
     In addition to the problems already mentioned, all cube and brick modules have at least two more detractions. First, none of these modules are particularly attractive. These known cube and brick modules, which incorporate at least three distinct types of faces, lack the aesthetic appeal of symmetry. They achieve limited functionality, but they are not beautiful structures in and of themselves. The second detraction of cube and brick blocks is that their space-filling orientations are rather mundane and uninteresting. Their possible building directions are up, down, left, and right. These blocks cannot connect at more novel angles, such as 45 degrees upward and to the right. 
     “Facially-Symmetric” Construction Modules 
     Construction modules with symmetric faces are also known in the prior art. Several U.S. Patents (U.S. Pat. Nos. 5,098,328, by Bierens—Mar. 24, 1992; 6,439,571, by Wilson—Aug. 27, 2002; and D359,315, by Tacey—Jun. 13, 1995) describe cube blocks with “six face symmetry.” All of these blocks&#39; faces are identical, which allows any face on one of these blocks to connect with any face on another identical block. 
     These blocks represent improvements over the aforementioned cubes and bricks, in that their connectability is more versatile. Their symmetry also renders them more aesthetically appealing. However, the overarching problem with these prior art “facially symmetric” building blocks is that none of their designs can be easily manufactured as one piece of plastic, using straight-pull injection molding processes. For example, Beerens&#39; patent suggests a method by which his cubes might be manufactured as six separate pieces, which must then be assembled before use. 
     Hollister describes a somewhat similar plan for a tetrahedron building block with symmetrical faces in his U.S. Pat. No. 6,152,797 (Nov. 28, 2000). Hollister&#39;s patent showed how his tetrahedron block might be manufactured as four separate triangular faces and four separate insertable connectors—eight pieces in all. In addition to the cost involved, this required assembly is troubling because it limits the materials that can be used to create these modules; some resins are not easily joined. Furthermore, there is always a danger of these complex modules coming apart, creating safety hazards. 
     Non-Box Shaped Construction Modules 
     Most prior art construction modules are box-shaped. Construction modules with other polyhedral geometries have represented a significant challenge to inventors. The advantage of these non-box-shaped building blocks is that they are not limited to vertical and lateral connections. Their faces do not necessarily lie parallel or perpendicular to one another. However, the same interesting geometry that has made them enticing candidates for building blocks has also rendered them impossible to manufacture economically. They have proven especially difficult to manufacture as one piece of material. Hollister&#39;s tetrahedron, mentioned in the previous paragraph, provides one example of this difficulty. In U.S. Pat. No. 7,247,075 (Jul. 24, 2007) Von Oech describes a golden right rhombic pyramidal polyhedron that can be manufactured as two pieces of material, plus multiple magnets. In U.S. Pat. No. 5,501,626 (Mar. 26, 1996), Harvey describes polygonal pieces that may be snapped together at their edges to create polyhedra. 
     Lalvani (U.S. Pat. No. 4,723,382) discloses an icosahedral system of ten polygonal members that may be assembled to create polyhedra as well as planar shapes. Lalvani&#39;s basic polygon members may be solid or “open lattice[s].” While Lalvani does disclose a means of connecting multiple panels or lattices to create polyhedra, he does not offer an easily manufactured integral polyhedron. In addition to the art of Lalvani and the others mentioned above, many other such polyhedra, which are constructed from individual, snap-together faces, are known. 
     Many other polyhedron inventors do not even address the issue of manufacturing. Evans (U.S. Pat. No. 6,257,574) discloses a variety of multi-polyhedral puzzles, where polyhedral blocks abut to form larger structures. Evans shows many configurations and enumerates many geometric specificities of polyhedral blocks, but he does not focus on how those blocks are made. 
     Viewed collectively, the prior art in construction modules suggests a clear failure to create construction modules with all of the following properties: one-piece, straight-pull, injection moldability; overall aesthetic appeal; compatible connectivity in a variety of directions; and a wide variety of possible polyhedral embodiments. 
     3. Objects and Advantages 
     Accordingly, it is the object of my invention to provide a variety of novel construction modules, each with a broad combination of advantages unknown in the prior art. 
     A first object of my invention is to provide some identical construction modules that can form aligned, face-to-face connections where one planar surface “matches up” and abuts with a compatible surface. 
     A second object of my invention is to provide some sets of construction modules that are space-filling. In other words, these sets of construction modules can tessellate, fully occupying the cells of a geometric honeycomb. 
     A third object of my invention is to provide construction modules that can be manufactured as a single piece of material, by a straight-pull injection mold. Such modules have reduced tooling costs, require no assembly, and cannot come unassembled. One-piece modules may also be manufactured in a variety of materials, some of which may pose and assembly problems to a multiple part module. 
     A fourth object of my invention is to provide some construction modules with unique geometries that transcend the common box shape. 
     A fifth object of my invention is to provide construction modules that are easily scalable, so that they may satisfy a variety of uses and age groups. A change of scale can also address a number of other manufacturing concerns, such as loose machining tolerances. 
     A sixth object of my invention is to provide individual modules with interesting symmetries. In a set of my modules, each individual module in a set has interesting symmetry, all by itself. Each can stand alone as a geometric work of art. Furthermore, when my individual modules are mated together, fascinating and continuous symmetry patterns emerge across multiple modules. 
     A seventh object of my invention is to provide connectively compatible construction modules of differing geometries. For example, some of my embodiments having surfaces coplanar with cubooctahedral, truncated octahedral, and truncated tetrahedral template can be made to fit together in a 3-D tessellation. Connective compatibility also allows variety of modules to be used together as a construction system. In this way, an animal sculpture could have a body made from isosceles tetrahedra and four legs constructed from sets of cubes. 
     A final object of my invention is to provide construction modules that can be made releasably connectable. All of my embodiments are designed in such a way that snap-fit connectors may be incorporated into their surfaces. The obvious advantage conferred by such connectability is that complex and semi-permanent structures can be built. 
     Further objects and advantages of my invention will become apparent from a consideration of the drawings and ensuing descriptions. 
     SUMMARY 
     My invention is a family of construction modules having two symmetric sets of surfaces. A construction module comprises a first and a second set of mating walls, each set having n-order rotational symmetry about a vertical linear axis. Each set consists of n subsets of mating walls, and each subset occupies a circular sector around the vertical linear axis. The cylindrical sector occupied by each subset is no greater than 180°/n. The first set of surfaces is mappable onto the second set of surfaces by a reflection across a horizontal plane followed by a 180°/n rotation about the vertical linear axis. In the preferred embodiments, at least one set of surfaces lies coplanar with a set of surfaces of a space-filling polyhedron template. Accordingly, a plurality of my modules may be abutted, face to face, to fill space. Furthermore, when viewed along the vertical linear axis, all mating walls are wholly visible. Thus, these modules may be molded as a single piece of plastic with a straight-pull injection mold whose axis of pull parallels the vertical linear axis. 
    
    
     
       DRAWINGS—FIGURES 
         FIG. 1A  is a perspective view of my preferred embodiment. 
         FIG. 1B  is a top view of my preferred embodiment. 
         FIG. 1C  is a side view of my preferred embodiment. 
         FIG. 1D  is a front view of my preferred embodiment. 
         FIG. 1E  is a top view of my preferred embodiment. 
         FIG. 1F  is a perspective view of a first set of mating walls of my preferred embodiment. 
         FIG. 1G  is a front view of a first set of mating walls of my preferred embodiment. 
         FIGS. 1H-1K  are perspective views illustrating the geometry of the mating walls of my preferred embodiment 
         FIG. 1L  is a perspective view showing the polyhedral template for my preferred embodiment 
         FIGS. 2A-2C  are perspective views showing how my preferred embodiment modules mate together. 
         FIGS. 2D and 2E  are perspective views of a thicker-walled version of my preferred embodiment. 
         FIG. 2F  is a perspective view of a tetrahedral structure comprising 96 aligned iterations of the preferred embodiment&#39;s polyhedron template. 
         FIG. 2G  is a perspective view of a cat sculpture comprising iterations of the preferred embodiment. 
         FIGS. 3A and 3B  are perspective views of my first alternative embodiment. 
         FIGS. 3C and 3D  are top and bottom views, respectively, of my first alternative embodiment. 
         FIGS. 3E-3H  are perspective views of multiple versions of my first alternative embodiment, mated together. 
         FIGS. 3I-3M  are illustrations explaining the geometry of my first alternative embodiment. 
         FIGS. 3N-3S  are perspective views of modules created by moving the mirror plane of my first alternative embodiment. 
         FIGS. 4A-4C  show my second alternative embodiment. 
         FIGS. 4D-4G  show how my second alternative embodiments mate together. 
         FIGS. 4H-4L  are illustrations explaining the geometry of my second alternative embodiment. 
         FIGS. 5A-5C  show my third alternative embodiment. 
         FIGS. 5D-5H  are illustrations explaining the geometry of my third alternative embodiment. 
         FIGS. 5I-5J  show how my third alternative embodiments mate together. 
         FIGS. 5K-5O  show a variant of my third alternative embodiment. 
         FIGS. 6A-6E  show my fourth alternative embodiment 
         FIGS. 7A-7D  show my fifth alternative embodiment. 
         FIG. 8A  shows my sixth alternative embodiment. 
         FIGS. 8B-8D  show how my fourth, fifth, and sixth alternative embodiments mate together and fill space. 
         FIGS. 9A-9C  show my seventh alternative embodiment. 
         FIGS. 9D and 9E  show my eighth alternative embodiment. 
         FIGS. 9F and 9G  show my ninth alternative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Preferred Embodiment—FIGS.  1 A- 1 K 
       FIG. 1A  is a perspective view of the preferred embodiment, module  20 , and its vertical linear axis  21 . Module  20  has 2 nd  order rotational symmetry about the vertical linear axis. For module  21 , n=order of rotational symmetry=2.  FIG. 1A  shows four mating surfaces or mating walls  22 ,  24 ,  26 , and  28 . The mating walls are so named because they are the portions of module  20  that mate, face to face, with other construction modules. Also shown in  FIG. 1A  are ancillary walls  23 ,  25 ,  27 , and  29 . The ancillary walls connect the mating walls and facilitate injection molding of the module. 
       FIGS. 1B  (top view),  1 C (side view), and  1 D (side view) teach the geometry of module  20 .  FIG. 1B  (vertical linear axis  21  coming out of the page) shows the n-order (2 nd  order) rotational symmetry of module  20 . It can be seen in these diagrams that mating walls  22  and  26  are 360°/n rotations of one another around the vertical linear axis  21 . Thus, mating walls  22  and  26  form a first set having n-order rotational symmetry about the vertical linear axis  21 . Mating walls  24  and  28  form a second set of mating walls. 
       FIGS. 1C and 1D  show that mating walls  22  and  26 , and mating walls  24  and  28 , are inclined obliquely to the vertical linear axis  21 . 
       FIG. 1E  (another top view) shows two circular sectors  30 . Each circular sector  30  encloses 90°. Circular sectors  30  illustrate an important characteristic of mating walls  22  and  26 . When viewed along the vertical linear axis  21  (as in  FIG. 1E ), mating wall  22  and mating wall  26  both lie completely inside their corresponding circular sector  30 . In general terms, mating wall  22  and mating wall  26  each lie completely inside a circular sector enclosing an arc of 180°/n)(90°. 
     Finally, it can be understood from  FIGS. 1A-1E  that the first set of mating walls  22  and  26  may be mapped onto the second set of mating walls  24  and  28  via two geometric transformations. This may be accomplished by first reflecting mating walls  22  and  26  across a horizontal mirror plane and by next rotating their images 180°/n(90°) about the vertical linear axis  21 . 
     The geometric relationship between the first set of mating walls  22  and  26  and the second set of mating walls  24  and  28  is made clearer in  FIGS. 1F-1I .  FIG. 1F  is a perspective view of mating walls  22  and  26  as they would appear if they were extracted from module  20 . In other words, they appear as they do in the module, but the rest of the module is invisible. The vertical linear axis  21  can still be seen.  FIG. 1G  (side view) shows the same material as what is shown in  FIG. 1F , plus the addition of a horizontal mirror plane  32 .  FIGS. 1H  (perspective view) and  1 I (side view) show what happens when mating walls  22  and  26  are reflected across horizontal mirror plane  32  (mirror plane  32  depicted only in  FIG. 1I ). Finally,  FIGS. 1J  (perspective view) and  1 K (side view) show what happens when the reflected “images” are rotated 90° about vertical axis  21 . It can be seen that the mating walls  22 ,  24 ,  26 , and  28  of  FIG. 1J  are the same as those of module  20  in  FIG. 1A . 
     In summary,  FIGS. 1F-1K  illustrate that the first set of walls  24  and  28  represent a reflection and a rotation of the second set of mating walls  22  and  26 . This reflection is across a horizontal mirror plane, and this rotation is a 180°/n rotation about the vertical linear axis (where n=2 for the preferred embodiment module  20 ). 
       FIGS. 1A  (perspective) and  1 B (top view—along vertical linear axis  21 ) can be used to understand the ancillary walls  23 ,  25 ,  27 , and  29 . The ancillary walls bridge the gaps between mating walls that appear adjacent when module  20  is viewed along the vertical linear axis  21 . In  FIG. 1B , mating wall  22  appears adjacent to mating wall  24 . Ancillary wall  23  connects the most clockwise edge of mating wall  22  with the most counter-clockwise edge of mating wall  24 . Likewise, ancillary wall  25  bridges the gap between adjacent mating walls  24  and  26 . Ancillary wall  27  bridges the gap between adjacent mating walls  26  and  28 . And, finally, ancillary wall  29  spans the gap between adjacent mating walls  28  and  22 . 
     In  FIG. 1B  (top view), the ancillary walls are shown on edge. This perspective shows that all of the ancillary walls are substantially vertical in the embodiment of module  20 . 
     It can be understood from the figures that this module  20  was designed to have characteristics of an isosceles tetrahedron.  FIG. 1L  shows a single mating wall  22  with a superimposed isosceles tetrahedral template  19 . An isosceles tetrahedron is a desirable template for a construction module, because it can tessellate and fill space. The inclinations of mating walls  22 ,  24 ,  26 , and  28 , relative to the vertical linear axis, were chosen so that those mating walls would be coplanar with the surfaces of a superimposed isosceles tetrahedral template. 
     It is important to not that the mating walls could have been inclined to the vertical linear axis  21  at any oblique angle. The module could still have been created, and it would still have “worked.” Furthermore, any mirror plane would have “worked,” but the particular mirror plane that was chosen was selected so that every mating wall would be coplanar with a hypothetical superimposed isosceles tetrahedral template. 
     HOW TO MAKE THE PREFERRED EMBODIMENT. The following is an alternative, “how-to,” narrative explaining the method of creating the preferred embodiment. 
     First, define the vertical linear axis  21  and select a polyhedral template  19  ( FIG. 1L , perspective view) with rotational symmetry. Orient the template so that it has rotational symmetry about the vertical linear axis  21 . Determine the order of the template&#39;s rotational symmetry, and set n equal to that order. In the case of module  20  the template  19  has 2 nd  order rotational symmetry about the vertical linear axis  21 , so n=2. Create a mating wall  22  that is coplanar with a wall of the template. Adjust mating wall  22  so that, when viewed along vertical linear axis  21 , mating wall  22  does not extend beyond a 180°/n circular sector  30  ( FIG. 1E , top view). Create another mating wall  26  that is a 360°/n rotation of mating wall  22  about the vertical linear axis  21  ( FIGS. 1F , perspective view and  1 G, side view). Create a second pair of mating walls  24  and  28  ( FIGS. 1H , perspective view; and  1 I, side view). Mating walls  24  and  28  must represent a reflection plus a rotation of mating walls  22  and  26 . To establish these mating walls, reflect mating walls  22  and  26  across a horizontal mirror plane  32 , and then rotate them 180°/n (here n=2) about the vertical linear axis  21 . The transition from  FIGS. 1H and 1I  to  FIGS. 1J and 1K  illustrates this rotation. This compound geometric transformation will map mating walls  22  and  26  onto the positions of the new mating walls  24  and  28 . Please note that, in this case, the horizontal mirror plane  32  passes through the midpoint of the hypotenuse of mating wall  24 . 
     Once these mating walls are established, the essence of this invention is in place. The remainder of the module design requires no special skill. Next, understand that the module  20  will be molded with an axis of mold pull paralleling the vertical linear axis  21 . While viewing the mating walls along this axis, determine which mating walls appear adjacent from this viewpoint. Provide an ancillary wall that bridges the gap between the edges of each pair of mating walls that appear adjacent from this viewpoint. The method above ensures that the mating walls will not present undercuts with this axis of mold pull. Care must still be taken to not add ancillary walls that will create undercuts. This is, however, a relatively simple task requiring no special skill. 
     OPERATION—PREFERRED EMBODIMENT 
     FIGS.  2 A- 2 G 
     End-User Operation 
     The end-user purpose of my invention is to provide a set of construction modules that can be mated together, face-to-face to create interesting patterns. 
       FIG. 2A  (perspective view) shows two identical modules  20  poised for mating. Mating wall  24  on the left hand module is ready to mate with mating wall  26  of the right hand module. It is important to notice that mating surfaces  24  and  26  are mirror images of one another. This is what makes face to face mating possible; mirror images may always be matched up in at least one orientation. 
       FIG. 2B  (perspective view) shows what happens after the two modules  20  of  FIG. 2A  have mated. 
       FIG. 2C  (perspective view) shows a collection of twenty-four identical modules  20 , which have been mated together to fill space. Their overall shape is a rhombic dodecahedron. 
     Manufacturing Operation 
     One extremely important operational aspect of my modules  20  pertains to their ability to be molded in one piece with a straight-pull injection mold. It can be understood from  FIG. 1A  and  FIG. 1B  (top view) that module  20  may be molded with an axis of mold pull paralleling the vertical linear axis  21 . Along this axis, there are no undercuts, so injection molding is possible with a straight-pull mold. This virtue stems from the facts that 1) each mating surface occupies no more than a 180°/n circular sector when viewed along the vertical linear axis  21  and 2) the mating walls  24  and  28  represent 180°/n rotations of mating walls  22  and  26 . This arrangement keeps the mating walls from “blocking one another” when viewed along the vertical linear axis  21 .  FIG. 1B  (top view) provides a perspective parallel to the anticipated direction of mold pull (along the vertical linear axis). From this perspective, all of the mating walls are visible. This would also be true of a bottom view. In either direction along the vertical linear axis, all of the mating walls are visible to an observer. This visibility ensures moldability without undercuts. The remainder of the module, the ancillary walls, all lie essentially parallel to the vertical linear axis and therefore do not create molding undercuts. 
     Moldability as a single piece of material makes these modules economical as well as safe; they have no assemblies that must be put together and that may later come apart. One-piece moldability also allows my modules to be manufactured in a variety of materials, some of which might be very good materials for toys, but which might also be very difficult to bond in a multiple-part toy. 
     For simplicity, the preferred embodiment module  20  has been depicted with very thin walls. In actual manufacture, however, the walls would have substantial thickness. It is very easy to modify the design shown here to achieve the thin and even wall thicknesses that are most suitable for injection molding.  FIGS. 2D and 2E  are perspective views of a module  20  with even wall thicknesses suitable for injection molding.  FIG. 2F  shows a plurality (ninety-six) of these thicker-walled modules  20  forming four rhombic dodecahedra, which are, in-turn forming a tetrahedral structure.  FIG. 2G  shows a plurality of these modules  20  mated together to form a cat. 
     First Alternative Embodiment 
     FIGS.  3 A- 3 D 
       FIGS. 3A-3D  show a first alternative embodiment, module  33 , having 3 rd  order symmetry. For module  33 , n=the order of symmetry=3. Module  33  has two sets of mating walls. The first set comprises n mating walls  34 ,  38 , and  42 . The second set of mating walls comprises another n mating walls  36 ,  40 , and  44 . The second set is a 360°/n rotation of the first set.  FIG. 3A  (side perspective view) shows a vertical linear axis  46 . It can be understood from  FIGS. 3A and 3C  (top view) that the first set of mating walls  34 ,  38 , and  42  has n-order symmetry about the vertical linear axis  46 . In the case of module  30 , the first set of mating walls  34 ,  38 , and  42  are inclined obliquely to the vertical linear axis  46 . Their angle of inclination is approximately 35.3°. 
     By examining  FIGS. 3A and 3C , in addition to  FIG. 3B  (bottom perspective) and  FIG. 3D  (bottom view), it can be confirmed that the second set of mating walls  36 ,  40 , and  44  represent a reflection plus a rotation of the first set of mating walls  34 ,  38 , and  42 . The first set is mappable onto the second set by reflection across a horizontal mirror plane and then a 180°/n (e.g. 60°) rotation about the vertical linear axis  46 . The reflection is indicated by a comparison of the top view of  FIG. 3C  with the bottom view of  FIG. 3D . These two views show that the two sets of mating walls are mirror images of one another. The 60° rotation is observable in these same figures, as the two sets of mating walls appear staggered in top and bottom views. They are offset in these top and bottom views by 60°. 
       FIG. 3C  (top view) shows on-edge views of ancillary walls  35 ,  37 ,  39 ,  41 ,  43 , and  45 . These ancillary walls are shown on edge. From this perspective, those ancillary walls can be understood to join adjacent mating walls. Please note that this adjacency is determined from a perspective along the vertical linear axis  46 . Thus both the top and bottom views of  FIGS. 3C and 3D  show the ancillary walls to be bridging the gaps between adjacent mating walls. 
     It is readily apparent from  FIGS. 3A-3D  that the inclinations of the mating walls in this embodiment were chosen to give the module  33  a cubical structure. Accordingly, the module  33  can mate with other such modules to form structures that can be built with cubes. 
     Furthermore, this embodiment has been depicted in  FIGS. 3A-3D  as having snap connectors. While snap connectors are not part of the present invention, these drawings show that they may readily be incorporated into these modules. 
     FIGS.  3 I- 3 M 
     The essence of this invention may also be understood from  FIGS. 3I-3M . These figs may serve as a “how-to” manual explaining the method behind the placements of mating walls  34 ,  36 ,  38 ,  40 ,  42 , and  44 . 
     First, a polyhedron template  31  was chosen because it has that has rotational symmetry ( FIG. 3I , perspective view). The template  32  was oriented so that it has rotational symmetry about the vertical linear axis  46 . The order of rotational symmetry of the template  31  was determined to be 3 rd  order. The value of “n” was established to be 3 (the order of rotational symmetry). 
     Second, a mating wall  34  was created such that it is coplanar with one of the surfaces of the template  31 . The size of the mating wall  34  was restricted so that it occupies a circular sector no greater than 180°/n(60°) when viewed along the vertical linear axis.  FIG. 3J  (top view) shows a view along the vertical linear axis  46 . A circular sector  61  enclosing 180°/n=60° is shown.  FIG. 4I  shows that mating wall  34  fits within circular segment  71 . 
     Third, two more mating walls  38  and  42  were established by rotating mating wall  34  multiples of 360°/n about the vertical linear axis  46  ( FIG. 3K , perspective view). This was repeated until a first set of mating walls had n order rotational symmetry about the vertical linear axis  46 . 
     Fourth, a second set of mating walls was created such that the second set was mappable onto the first set. This was done by first reflecting the first set of mating walls  34 ,  38 , and  42  across a horizontal mirror plane ( FIG. 3L , perspective view). In  FIG. 3L , the approximate position of the mirror plane is indicated by a broken line  72 . Please note that, in this case, the mirror plane passes through the midpoint of the leg of mating wall  34  that is most distant from the vertical linear axis  46 . In addition to this reflection, the first set of mating walls was also rotated 180°/n about the vertical linear axis  46 .  FIG. 3M  (perspective view) shows the effect of rotating the first set of mating walls from their reflected positions in  FIG. 3L  to the actual positions of mating walls  36 ,  40 , and  44 . 
     The final step in transforming the parts of  FIG. 3M  into the moldable module of  FIGS. 3A-3D  requires no special skill. One simply accepts that the direction of mold pull will be parallel to vertical linear axis  46 , and then one adds ancillary walls or “filler” to connect the mating walls. This must be done in a way that prevents undercuts from appearing, but it is not a difficult task. 
     Variations on this Embodiment 
     FIGS.  3 N- 3 S 
     Module  33  of  FIGS. 3A-3F  are essentially cubical. This is the case because the proper horizontal mirror plane  72  was chosen ( FIG. 3L ). The modules of  FIGS. 3N-3S  show how new modules may be created simply by altering this horizontal mirror plane. The module of  FIG. 3N  was produced by moving the horizontal mirror plane downward from its position in  FIG. 3L .  FIG. 3O  is a top view of the module of  FIG. 3N .  FIG. 3P  shows four of these modules mated together. Interestingly, these modules still exhibit cubic space-filling properties. 
     The module of  FIG. 3Q  was produced by moving the horizontal mirror plane upward from its position in  FIG. 3L .  FIG. 3R  is a top view of the module of  FIG. 3Q .  FIG. 3P  shows four of these modules mated together to form a tetrahedral structure. 
     First Alternative Embodiment 
     FIGS.  3 E- 3 H 
       FIGS. 3E and 3F  (both perspective views) show that individual modules  30  of this embodiment can mate in two different ways. As is true will all of the embodiments of this invention, the minor-image mating walls of the first and second mating wall sets can mate face-to-face. In addition, since the mating walls of these cuboidal modules have minor symmetry, any mating wall may be mated with any other mating wall.  FIG. 3E  shows the pattern that results when a mating wall of the first set ( 36 ,  40 , or  44 ) mates face to face with a mating wall of the second set ( 34 ,  38 , or  42 ).  FIG. 3F  shows the pattern that results when a mating wall mates face to face with a mating wall of its own set (albeit, on a different module).  FIGS. 3G and 3H  are perspective views showing multiple versions of module  46 , mated together to fill space. 
       FIGS. 3A-3D  also show that module  33  may be molded with a straight pull mold whose axis of mold pull parallels the vertical linear axis  46 .  FIG. 3C  (top view) provides a perspective parallel to the anticipated direction of mold pull (along the vertical linear axis). From this perspective, all of the mating walls are visible. This would also be true of a bottom view. In either direction along the vertical linear axis, all of the mating walls are visible to an observer. This visibility ensures moldability without undercuts. 
     Second Alternative Embodiment 
     FIGS.  3 A- 3 C 
       FIG. 4A  (perspective view) and  FIG. 4C  (top view) show a module  47  with n-order (n=2) rotational symmetry about a vertical linear axis  56 . Module  47  has a first set of mating walls,  48  and  52  which are inclined to the vertical linear axis  56  at an angle of approximately 45°. These mating walls are circular in shape. This first set of mating walls has n-order rotational symmetry about the vertical linear axis  56 . Furthermore each mating wall  48  and  52  occupies a circular sector, when viewed along the vertical linear axis  56 , no greater than 180°/n. 
     Module  47  has a second set of mating walls  50  and  54 , which are mappable onto the first set of mating walls by a reflection across a horizontal mirror plane plus a 180°/n rotation about the vertical linear axis  56 . 
       FIG. 4D  (perspective view) shows two modules  47  with superimposed isosceles tetrahedra. This figure shows that every mating wall of this module is coplanar with a surface of a hypothetical superimposed isosceles polyhedron. 
     Method Description 
     FIGS.  4 H- 4 K,  4 A,  4 C 
     The true nature of this invention may also be understood from  FIGS. 4H-4K , which serve as a “how-to” manual explaining the method behind the placements of mating walls  48 ,  50 ,  52 , and  54 . 
     First, select a polyhedron template  58  ( FIG. 4H , perspective view) that has rotational symmetry. Then orient the template  58  so that it has rotational symmetry about the vertical linear axis  56 . Determine the order of rotational symmetry of the template  58 . In  FIG. 4H , the template  58  has 2 nd  order rotational symmetry about the vertical linear axis  56 , so record order of rotational symmetry as n=2. 
     Second, create a mating wall  48  that is coplanar with one of the surfaces of the template  58 . Restrict the size of the mating wall  48  so that it occupies a circular segment no greater than 180°/n when viewed along the vertical linear axis.  FIG. 4I  (top view) shows a circular sector  59  enclosing 180°/n(90°).  FIG. 4I  shows that mating wall  48  fits within circular segment  59 . The mating wall  48  is circular, though it appears ovoid due to the perspective of this figure. 
     Third, create a second mating wall  52 , such that it is a 360°/n rotation of mating wall  48  about the vertical linear axis  56 .  FIG. 4J  (perspective view) shows this relationship. This ensures that mating walls  48  and  52  are a “first set” with n-order rotational symmetry about the vertical linear axis  56 . 
     Fourth, create another set of mating walls  54  and  50  that is mappable onto mating walls  48  and  52 . Do this by first reflecting mating walls  52  and  48  across a horizontal mirror plane. This reflection is shown in  FIG. 4K  (perspective view). The horizontal mirror plane is represented in this diagram as broken line  60 . In addition to reflecting the mating walls, rotate them 180°/n about the vertical linear axis  56 .  FIG. 4L  (perspective view) shows the effect of rotating the mating walls from their reflected positions in  FIG. 4K  to the actual positions of mating walls  54  and  50 . 
       FIG. 4L  also shows the superimposed template  58 . Notice that all of the mating walls are coplanar with surfaces of the template. By comparing this figure with  FIGS. 4A-4C , one can see that  FIG. 4L  does show the same relative positions of the mating walls of module  47 . 
     The final step in transforming the mating walls of  FIG. 4L  into the moldable module of  FIG. 4A  requires no special skill. A designer must simply acknowledge that the direction of mold pull will be parallel to vertical linear axis  56 . Then one must add ancillary walls or “filler” to connect the mating walls. This must be done in a way that prevents undercuts from appearing, but it is not a difficult task. 
     Second Alternative Embodiment 
     FIGS.  4 D- 4 G 
       FIGS. 4D-4G  show that the multiple versions of module  47  can mate face to face and fill space in the manner of isosceles tetrahedra. Isosceles tetrahedra are shown superimposed over the modules in these figures. 
       FIGS. 4A-4C  make it apparent that module  47  may be molded with a straight pull mold whose axis of mold pull parallels the vertical linear axis  56 .  FIG. 4C  (top view) provides a perspective parallel to the anticipated direction of mold pull (along the vertical linear axis). From this perspective, all of the mating walls are visible. This would also be true of a bottom view. In either direction along the vertical linear axis, all of the mating walls are visible to an observer. This visibility ensures moldability without undercuts. 
     Third Alternative Embodiment 
     FIGS.  5 A- 5 H 
       FIGS. 5A  (Perspective View),  5 B (top view), and  5 C (bottom view): A construction module  62  has a first set of mating walls  64 ,  66 ,  74 , and  76  and a second set of mating walls  68 ,  70 ,  78 ,  80 . The purpose of these mating walls is to “match up,” face to face, with other modules, during construction. Module  62  also has ancillary walls  63 ,  67 ,  69 ,  71 ,  73 ,  75 ,  77 , and  79 . The ancillary walls serve to connect the mating walls and to facilitate injection molding. Additionally, module  62  has cosmetic walls  81 ,  83 ,  85 ,  89 ,  91 ,  93 ,  95 , and  97 . These cosmetic walls are not absolutely necessary, but they give the module  62  the look of a polyhedron. They also increase the surface area that abuts when two modules are mated together, face to face. 
     Third Alternative Embodiment 
     FIGS.  5 D- 5 H 
     The essence of this invention may also be understood from  FIGS. 5D-5H . These figs may serve as a “how-to” manual explaining the design method behind the placements of the mating walls of module  62 . 
     First, a polyhedron template  63  was chosen because it has that has rotational symmetry ( FIG. 5D , perspective view). The template  63  was oriented so that it has rotational symmetry about the vertical linear axis  84 . Template  63  is a truncated isosceles tetrahedron. The order of rotational symmetry of the template  63  was determined to be 2 nd  order. The value of “n” was established to be 2 (the order of rotational symmetry). 
     Second, a first subset of mating walls was created such that those mating walls were coplanar with surfaces of the template  63 . This first subset consists of mating walls  64  and  66 . Mating wall  64  is a half of a hexagonal face of a truncated isosceles tetrahedron. Mating wall  66  is a half of a triangular face of a truncated isosceles tetrahedron. The overall size of this first subset was restricted so that it occupies a circular sector no greater than 180°/n(90°) when viewed along the vertical linear axis  84 .  FIG. 5E  (top view) shows the first subset (mating walls  64  and  66 ) from a view along the vertical linear axis  84 . A circular sector  82  enclosing 180°/n=90° is shown.  FIG. 5E  shows that the subset consisting of mating walls  64  and  66  fits within circular segment  82 . 
     Third, a second subset of mating walls was established by rotating the first subset multiples of 360°/n about the vertical linear axis  84  ( FIG. 5F , perspective view). This was repeated until a first set of mating walls had n order rotational symmetry about the vertical linear axis  84 . In this case, the 2 nd  order symmetry requires a total of only two subsets. The second subset consists of mating walls  74  and  76 . Together, these two subsets comprise a first set of mating walls  64 ,  66 ,  74 , and  76 . 
     Fourth, a second set of mating walls was created such that the second set was mappable onto the first set. This was done by first reflecting the first set of subsets (mating walls  64 ,  66 ,  74 , and  76 ) across a horizontal mirror plane ( FIG. 5G , perspective view). In  FIG. 5G , the approximate position of the mirror plane is indicated by a broken line  86 . If a superimposed truncated isosceles tetrahedral template had been shown in this figure, mirror plane  86  would have passed through its vertical midpoint [“vertical midpoint” means half way between the lowest point and the highest point]. In addition to this reflection, the first set of mating walls was also rotated 180°/n about the vertical linear axis  84 .  FIG. 5H  (perspective view) shows the effect of rotating the first set of mating walls from their reflected positions in  FIG. 5G  to the actual positions of mating walls  68 ,  70 ,  78 , and  80 . 
     The final step in transforming the parts of  FIG. 5H  into the moldable module of  FIGS. 5A-5C  requires no special skill. One simply accepts that the direction of mold pull will be parallel to vertical linear axis  84 , and then one adds ancillary walls or “filler” to connect the mating walls. 
       FIG. 5A  shows that additional cosmetic walls  81 ,  83 ,  85 ,  89 ,  91 ,  93 ,  95 , and  97  must also be added. These walls must be added in a way that prevents undercuts from appearing, but it is not a difficult task. 
     Alternatively, the cosmetic walls may be left out, producing the version of module  62  shown in  FIG. 5K . 
     Third Alternative Embodiment 
     FIGS.  5 I- 5 O and  5 A- 5 C 
       FIGS. 5I and 5J  (both perspective views) show two ways in which two modules  62  can mate face to face. In both of these views, one set of mating faces is visible on one module, while the other set is visible on the second module. In both figures, it can be seen that the first set of mating walls  64 ,  66 ,  74 , and  76  represents a mirror image of the second set of mating walls  68 ,  70 ,  78 , and  80 . From these diagrams, it is clear that this characteristic that allows the mating walls to be “matched up” face-to face. 
       FIGS. 5K-5O  show more ways in which modules  62  can mate with one another.  FIG. 5L  suggests a potential connection between mating walls  64  and  68 .  FIG. 5M  shows twenty-four modules connected together using this connection.  FIGS. 5N and 5O  show a connection such as that between mating walls  76  and  80 . 
       FIGS. 5A-5C  make it apparent that module  62  may be molded with a straight pull mold. The axis of mold pull is along the vertical linear axis  84  shown in  FIG. 5H . From either direction along the vertical linear axis, all of the mating walls are visible to an observer. 
     Fourth Alternative Embodiment 
     FIGS.  6 A- 6 E 
       FIGS. 6A  (perspective view),  6 B (top view), and  6 C (bottom view) show a module  100  with n-order (n=2) rotational symmetry about a vertical linear axis  101 . The angles of module  101  are based on a cubooctahedral template.  FIG. 6A  shows a first subset of mating walls  102 ,  104 , and  106 . Also shown is a second subset of mating walls ( 108 ,  110 , and  112 ) representing a 360°/n rotation of the first subset. Thus the two subsets form a first set with n-order rotational symmetry about the vertical linear axis  101 . 
     A second set of mating walls is also shown. This second set includes a first subset of mating walls  120 ,  122 , and  124 ; and a second subset of mating walls  114 ,  116 , and  118 . This second set of mating walls represents a geometric transformation of the first set of mating walls.  FIG. 6D  (side view) can be used to understand this transformation. The first set of mating walls  102 ,  104 ,  106 ,  108 ,  110 , and  112  may be mapped onto the second set by mirroring them across mirror plane  119  and then rotating them 180°/n about the vertical linear axis  101 . 
       FIGS. 6A-6C  also show ancillary walls  103 ,  105 ,  107 , and  109 , as well as cosmetic walls  111 ,  113 ,  115 , and  117 . 
     Fourth Alternative Embodiment 
     FIGS.  6 E,  8 B- 8 D 
       FIG. 6E  shows how a plurality of modules  101  may be mated together, face to face, to build an interesting structure.  FIGS. 8B-8D  demonstrate this module&#39;s ability to mate and fill space with truncated octahedral modules  125  and truncated tetrahedral modules  140 . 
     In either direction along the vertical linear axis, all of the mating walls are visible to an observer. Thus this module is moldable with a straight pull mold whose axis of mold pull parallels the vertical linear axis  101 . 
     Fifth Alternative Embodiment 
     FIGS.  7 A- 7 C 
       FIGS. 7A  (perspective view),  7 B (top view), and  7 C (side view) show a module  125  modeled after a truncated octahedral template. The module  125  has 2 nd  order rotational symmetry around a vertical linear axis  127 , so n=2 for this module. Module  125  has a first subset of mating walls  126 ,  128 , and  130  and a second subset of mating walls  132 ,  134 , and  136 . Mating wall  126  represents a half of a hexagonal face of a truncated octahedron, and mating wall  130  represents a half of another hexagonal face of the same truncated octahedron From the viewpoint of  FIG. 7B  (along the vertical linear axis  127 ) it is clear that both subsets fit in a circular sector of 180°/n)(90°). 
       FIG. 7C  (side view) shows a mirror plane  138 . The entire module can be mapped onto itself by a reflection across mirror plane  138 , followed by a 180°/n rotation about the vertical linear axis  127 . If a superimposed truncated octahedral template had been shown in this figure, mirror plane  138  would have passed through its vertical midpoint. 
     Fifth Alternative Embodiment 
     FIGS.  7 A- 7 D,  8 B- 8 D 
       FIGS. 7A-7C  demonstrate that module  125  is free of undercuts and can therefore be molded with a straight pull mold whose axis of mold pull is parallel to the vertical linear axis  127 . In either direction along the vertical linear axis, all of the mating walls are visible to an observer. 
       FIG. 7D  demonstrates the ability of a plurality of these modules to connect together, face to face.  FIGS. 8B-8D  demonstrate this module&#39;s ability to mate with and fill space with cubooctahedral modules  101  and truncated tetrahedral modules  140 . 
     Sixth Alternative Embodiment 
     FIGS.  8 A- 8 D 
     Module  140  is modeled after a regular truncated tetrahedron. It is similar to the truncated isosceles tetrahedral module  84  shown in  FIG. 5H . While regular truncated tetrahedra do not fill space on their own, they do fill space in concert with regular truncated octahedra and cubooctahedra.  FIGS. 8B-8D  demonstrate this module&#39;s ability to mate and fill space with cubooctahedral modules  101  and truncated octahedral modules  125 . 
     Seventh Alternative Embodiment 
     FIGS.  9 A- 9 C 
       FIG. 9A  is a top view of module  142 .  FIG. 9B  is a side view. Its vertical linear axis  143  is shown in both figures.  FIG. 9C  shows eight modules  142  mated together. 
     Eighth Alternative Embodiment 
     FIGS.  9 D- 9 E 
       FIG. 9D  shows a module  144  with mating walls coplanar with a superimposed cube. The module&#39;s vertical linear axis  145  is indicated.  FIG. 9E  shows multiple versions of module  144  mated together. 
     Ninth Alternative Embodiment 
     FIGS.  9 F- 9 G 
       FIG. 9F  shows a module  146 . The module&#39;s vertical linear axis  147  is indicated.  FIG. 9G  shows four modules  146  mated together. 
     CONCLUSION, RAMIFICATIONS, AND SCOPE 
     Thus the reader will see that the construction modules of this invention represent a combination of advantages unprecedented in the prior art. Each module may be straight pull molded as a single piece of material while retaining the face-to-face construction properties of a polyhedron. Accordingly, most of my modules may be intuitively mated to compatible modules occupying any or all of the adjacent cells of a geometric honeycomb. For my cube-derived embodiments, this means my modules can be built outward in any of six directions; up, down, left, right, back, and forth. For embodiments derived from an isosceles tetrahedron, this means building outward in four directions. In this way, my construction modules can substantially fill space and extend into space in three dimensions. Furthermore, my construction modules have additional advantages in that
         they function as polyhedra, any face of which can be mated to at least half of its identically-shaped faces on another identical polyhedron.   my invention is not limited to the embodiments shown here; it is a method of creating an unlimited number of interesting modules with a variety of characteristics.   they may be manufactured with an economical straight-pull injection mold.   any of my modules can be designed with injection moldable snap-fit connectors, thus rendering all of their mating configurations secure but releasable.   compared to most construction modules, many of my modules&#39; embodiments represent novel geometries, and their connections space-filling characteristics are therefore surprising, interesting, and challenging.   each of my modules can be designed to accept snap-fit accessories, such as eyes, on numerous surfaces.   my modules can serve as fascinating math-teaching manipulatives that are useful for teaching symmetry and tessellation concepts.   they may be manufactured at a number of scales, allowing them to satisfy a broad variety of aesthetic, functional, and safety criteria.   my modules&#39; connectors may be made compatible so that several embodiments of my modules might be sold together as a construction system of connectably compatible modules with a variety of geometric characteristics.       

     While my above description contains many specificities, these should not be construed as limitations on the scope of the invention, but rather as an exemplification of one preferred embodiment thereof. Many other variations are possible. For example,
         Variations of my construction modules may have different wall thicknesses.   My construction modules may have rounded edges and corners, rather than the sharp edges and corners shown in this document.   My modules surfaces may be carved away or added to in many different ways, either cosmetic, utilitarian, or both.   For any one polyhedron template, many module variations may be created, comprising polyhedron wall portions of varying sizes, shapes, and origins.   My modules may be made in a variety of sizes and colors—or in no color at all.   My modules may be made in a variety of plastic and non-plastic materials, such as plastic, wood, or metal.   My modules designs may be derived from a variety of polyhedron templates, including but not limited to the following geometries: cuboidal, regular tetrahedral, isosceles tetrahedral, regular octahedral, isosceles octahedral, truncated isosceles tetrahedral, truncated regular tetrahedral, truncated isosceles octahedral, truncated regular octahedral, cubooctahedral, brick-shaped, rhombus-shaped, and rhombic hexahedral.   My modules can be made with snap-fit or press fit connectors—or no connectors at all.   My modules can incorporate male and female connectors arranged in a variety of configurations.   The manner in which mating walls of my modules are connected together can vary; for instance, they can be connected with ribs, struts, portions of a spherical shell, or any type of ancillary wall. They may also simply connect at one or more of their edges, surfaces, or corners.   My modules may be used in sets of identical modules, or they may be used in sets of varied, but compatible, modules.   My modules may be used as toys or for other construction purposes.   My modules may be used whole or in part.       

     Thus the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their legal equivalents.