Abstract:
Panels can join to form a structural module via slotting, abutment, and rotational symmetry. The slots allow for assembly without additional fastening. Modules can range in shape and size, while conforming to the interlocking configuration between the panels. Panels can be joined to form various structures with similar connective features. The panel&#39;s combinability via the slots makes possible many structural forms and re-configurable applications.

Description:
FIELD OF THE INVENTION 
     The field to which the invention generally relates is static structures formed of single self-supporting panels. 
     BACKGROUND 
     Static structures formed from single self-supporting panels attachable to one another via one or more separate connecting means to form a structure are generally known in the art as shown in U.S. Pat. No. 4,719,726 and U.S. Pat. No. 7,434,359. It would be desirable to provide one or more generally planar panels attachable to one another without the need for additional separate connecting means to form a structure for the purpose of reducing the number of required parts for assembly; simplifying construction of a structure; and reducing the cost of manufacturing the structure. It would be desirable to provide a flat pack capability for ease of shipping and storage. It would be desirable for the module to be adaptable to many re-configurable applications. It would be desirable to provide for ease of disassembly and reassembly in a portable configuration, such as kits and as technology for building systems. 
     SUMMARY 
     As used herein the term “kit” is used generically to describe a system for building interlocking three dimensional shapes configured from triangular tessellations. A kit for building a structural shape can include at least one planar panel that can include at least three sides. The at least three sides can include a first side that can be a straight edge having a first end and a second end, a second side connected to the first end and extending from the first side at a first angle, and a third side connected to the first end and extending from the first side at a second angle. 
     The kit can further include a first, a second, and a third planar panel, where each planar panel can include at least three sides and each panel can be either identical in shape and size to one another to form regular modules, or non-identical as long as adjoining edges are equal in length to form irregular modules. The three sides can be straight, curved, or can vary in shape. The at least three sides of each panel can include a first side that can be a straight edge having a first end and a second end, a second side connected to the first end and extending from the first side at a first angle, and a third side connected to the first end and extending from the first side at a second angle. The kit can further include a first connector integrally formed with the first side of each panel and defining a first slot between the first side and the first connector having a first blind end substantially located at the midpoint of the first side. The first slot can be defined to be substantially parallel to the first side. The kit can further include a second connector integrally formed with the second side of each panel defining a second slot having a second blind end between the second side and the second connector. The second slot can be defined to be substantially parallel to the second side. The kit can further include a third connector integrally formed with the third side of each panel defining a third slot having a third blind end between the third side and the third connector. The third slot can be defined to be substantially parallel to the third side. 
     The second connector and third connector of each planar panel can mechanically engage with one another to define a three dimensional geometric shape, wherein the second slot of the second connector of the first planar panel slidably engages the third slot of the third connector of the second planar panel, the second slot of the second connector of the second planar panel slidably engages the third slot of the third connector of the third planar panel, and the second slot of the second connector of the third planar panel slidably engages the third slot of the third connector of the first planar panel, such that the second blind ends of each of the second slots abuts the third blind end of the third slot to mechanically interconnect the first planar panel, the second planar panel, and the third planar panel with respect to one another, such that a first joint is formed at the intersection of each planar panel and an adjacent planar panel to define at least one substantially tetrahedron-shaped assembled sub-structure hereinafter referred to as a module, which is a basis for a polyhedra, such as a platonic solid. 
     The at least one module structure can further include a first module structure, a second module structure, a third module structure, a fourth module structure, and a fifth module structure. The first connectors of the first through fifth module sub-structures can mechanically engage one another, such that one of the first blind ends of one of the first slots of the first sub-structure abuts one of the first blind ends of one of the first slots of an adjacent sub-structure, such that the first module sub-structure and the second through fifth adjacent module sub-structure are connectable with respect to one another. If five irregular shaped modules are used, the assembled structure can form at least one substantially pentagon-shaped structure. If six regular shaped modules are used, the assembled structure can form at least one substantially hexagonal-shaped structure. Rotational symmetry can be provided, where if the first slots are oriented in a like direction, the slots will interlock with respect to one another. Twelve pentagonal shaped structures can interlock to create a dodecahedron, which is a platonic solid. A plurality of hexagonal shaped structures can be interconnected but will not define a polyhedra, since the resulting shape is not totally enclosed due to the inclusion of square openings in the assembled structure. 
     The at least one substantially pentagonal shaped structure can further include a first substantially pentagonal shaped structure and a second substantially pentagonal shaped structure, wherein the first slot of the first connector of the a first substantially pentagonal shaped structure can slidably engage the first slot of the first connector of the a second substantially pentagonal shaped structure, such that the first blind end of each of the first slots abuts the first blind end of the first slot to mechanically interconnect the first substantially pentagonal shaped structure and second substantially pentagonal shaped structure to form at least one assembled modular structural shape. 
     The slot geometry and vertices of each panel can be modified to define the dimensions of a substantially tetrahedron-shaped module. Adjacent modules can be given identical lengths and touching edges, thus allowing the modules to tessellate and interconnect in such a way that a wide variety of forms can be achieved. 
     Other embodiments of the present invention will become apparent to those skilled in the art when the following detailed description is read in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The description herein makes reference to the accompanying drawings wherein like reference numerals refer to like parts throughout the several views, and wherein: 
         FIGS. 1A-1C  are side views of a set of irregularly shaped panels, where each panel has an optional lattice structure formed within an area defined by a peripheral edge, the peripheral edge defines at least a first straight edge, a second edge connected at a first angle with respect to the first edge, and a third edge connected at a second angle with respect to the first edge, and where vertices A-A, B-B, C-C of the set of panels connect to one another to form an assembled module; 
         FIG. 2A  is a plan view of an assembled generally tetrahedron-shaped modular structure formed of first, second, and third panels as illustrated in  FIG. 1A-1C  with three panels forming a three sided receptacle with an irregular triangular open end; 
         FIG. 2B  is a side view of the assembled generally tetrahedron-shaped modular structure illustrated in  FIG. 2A  and formed of first, second, and third panels as illustrated in  FIGS. 1A-1C ; 
         FIG. 2C  is a rotated side elevational view of the assembled generally tetrahedron-shaped modular structure as illustrated in  FIGS. 2A-2B  and formed of first, second, and third identical panels as illustrated in  FIGS. 1A-1B  illustrating a vertices joint between adjacent panels; 
         FIGS. 3A and 3B  illustrate a planar panel forming a regular equilateral panel from line A-B, A-D, and B-D without optional lattice structure; 
         FIGS. 4A-4C  illustrate a kit of three regular equilateral panels of  FIGS. 3A-3B  including a first planar panel, a second planar panel, and a third planar panel, where each planar panel is identical to each other with first, second, and third connectors slots and blind ends respectively for assembly into a module through interconnection of connectors A-A, B-B, C-C; 
         FIGS. 5A and 5B  illustrate a planar panel forming a regular equilateral panel from line A-B, A-D, and B-D, where the first, second, and third connectors can have a curved outer edge; 
         FIG. 6  is an exploded detail view of a first joint formed by connecting first and second panels; 
         FIG. 7  is a perspective view of an assembled generally pentagonal shaped structure formed of first, second, third, forth, and fifth assembled generally tetrahedron-shaped modular structures as illustrated in  FIGS. 2A-2C , where the tetrahedron-shaped modular structures are formed from a plurality of irregular panels; 
         FIG. 8  is a simplified perspective view of an assembled modular structure formed of a plurality of generally pentagonal shaped modular structures as illustrated in  FIG. 7 , where the tetrahedron-shaped modular structures are formed from a plurality of irregular panels; 
         FIGS. 9A-9C  illustrate the use of tetrahedron-shaped modular structures for assembling a larger superstructure; 
         FIG. 10A  illustrate a method or process for assembling a module from either regular or irregular shaped panels that fit together to form a triangular network as long as the vertices are contiguous; and 
         FIG. 10B  illustrates a method or process for assembling panels to one another through interconnection of the first connectors. 
     
    
    
     DETAILED DESCRIPTION 
     The terms “substantially”, “near”, and “about” as used within this application shall be construed to have their ordinary meanings. That is, “substantially”, “near”, and “about” shall be considered to mean “near, close to, not far from, or otherwise somewhere or something close to” that to which the terms relate. 
     At least one panel can be either regular or irregular and can make up modules that can be either regular or irregular, and can be fit together to form any triangular network as long as the vertices of adjacent panels and modules are contiguous. The modules allow construction of platonic solid shapes, such as a tetrahedron that can be the basis for a three panel module and the building of larger shapes with a plurality of tetrahedron modules, such as a dodecahedron. 
     Referring now to  FIGS. 1A-1C  a kit for building a structural shape  10  can include at least one planar panel  12  having at least three sides. The at least three sides can include a first side  14  formed as a straight edge having a first end  16  and a second end  18 , a second side  20  connected to the first end  16  and extending from the first side  14  at a first predetermined angle  22 , and a third side  24  connected to the first end  16  and extending from the first side  14  at a second predetermined angle  26 . 
     The second side  20  and third side  24  are defined by lines BD and AD respectively and can include straight edge portions, non-straight edge portions, and any combination thereof. The first side  14 , second side  20 , and third side  24  can each individually be of length and dimension suitable to define a generally triangular-shape, or generally trapezoidal-shape, of the at least one planar panel  12 . The at least three sides can include a fourth side, fifth side, and any number of other sides having straight edge portions, non-straight edge portions and any combination thereof, to define any desired shape extending between the second side  20  and third side  24 . 
     The first predetermined angle  22  can range from a minimum of approximately 10° to a maximum of approximately 160°, inclusive. The first predetermined angle  22  can more preferably range from a minimum of approximately 20° to a maximum of approximately 120°, inclusive. The first predetermined angle  22  can most preferably range from a minimum of approximately 30° to a maximum of approximately 70°, inclusive. The second predetermined angle  26  can range from a minimum of approximately 10° to a maximum of approximately 160°, inclusive. The second predetermined angle  26  can more preferably range from a minimum of approximately 20° to a maximum of approximately 120°, inclusive. The second predetermined angle  26  can most preferably range from a minimum of approximately 30° to a maximum of approximately 70°, inclusive. 
     Each panel of the kit can include a first connector  28  integrally formed with the first side  14  to define a first slot  30  between the first side  14  and the first connector  28  having a first blind end  32  substantially located at a midpoint of the first side  14 , with the first connector  28  having a straight edge between the second end  18  and an outer tip  28   a  of the first connector  28 . The first slot  20  can be defined to be substantially parallel to the first side  14 . As illustrated in  FIG. 1A , the first slot  30  has an open end facing away from the second end  18 . 
     Each panel of the kit can include a second connector  34  integrally formed with the second side  20  to define a second slot  36  having a second blind end  38  between the second side  20  and the second connector  34 . The second slot  36  can be defined to be substantially parallel to the second side  20 . As illustrated in  FIG. 1A , the second slot  36  has an open end facing away from the first end  16 . 
     Each panel of the kit can include a third connector  40  integrally formed with the third side  24  to define a third slot  42  having a third blind end  44  between the third side  24  and the third connector  40 . The third slot  42  can be defined to be substantially parallel to the third side  24 . As illustrated in  FIG. 1A , the third slot  42  has an open end facing toward the second end  18 . 
     Each of the first slot  30 , second slot  36 , and third slot  42  can be defined, respectively, by the first connector  28 , second connector  34 , and third connector  40 , such that the first slot  30 , second slot  36 , and third slot  42  are substantially similar in width, such that the width of each slot is substantially similar to the thickness of a planar panel and is capable of slidably engaging another planar panel. The first blind end  32 , second blind end  38 , and third blind end  44  define the ends of the first slot  30 , second slot  36 , and third slot  42 , respectively. 
     Referring now to  FIGS. 1A-2C , the kit can include a first planar panel  12   a , a second planar panel  12   b , and a third planar panel  12   c , each planar panel  12   a ,  12   b ,  12   c  being non-identical to each other with first, second, and third connectors  28 ,  34 ,  40 , slots  30 ,  36 ,  42 , and blind ends  32 ,  38 ,  44 , respectively. As best seen in  FIG. 2A , the second connector  34  and third connector  40  of each planar panel  12   a ,  12   b .  12   c  can mechanically engage with one another to define a three dimensional geometric shape, wherein the second slot  36  of the second connector  34  of the first planar panel  12   a  operably engages with the third slot  42  of the third connector  40  of the second planar panel  12   b  to define a first sliding joint. The first sliding joint can be formed by slidably engaging the second connector  34  and second slot  36  of the first planar panel  12   a  with the third connector  40  and third slot  42  of the second planar panel  12   b , such that the second blind end  38  of the first planar panel  12   a  abuts the third blind end  44  of the third slot  42  of the second planar panel  12   b , such that the second slot  36  is filled with the third connector  40 , the third slot  42  is filled with the second connector  34 , a portion of the third connector  40  overlies the second connector  34 , and a portion of the second connector  34  overlies the third connector  40 . As best seen in  FIG. 2A , the kit can include at least one planar panel  12 , and more particularly can include a first planar panel  12   a , a second planar panel  12   b , and a third planar panel  12   c.    
     Referring now to  FIGS. 1A-2C, and 10A , the second connector  34  and third connector  40  of each planar panel  12   a ,  12   b ,  12   c  can mechanically engage with one another to define a three dimensional geometric shape, i.e. vertex A of  FIG. 1A  connected to vertex A of  FIG. 1C ; vertex B of  FIG. 1A  connected to vertex B of  FIG. 1B ; and vertex C of  FIG. 1B  connected to vertex C of  FIG. 1C . In this way, the planar panels  12   a ,  12   b , and  12   c , come together at vertex D of each panel. The three dimensional geometric shape of  FIG. 2A  is defined by assembling the panels as shown in  FIG. 10A  with the second slot  36  of the second connector  34  of one of the planar panels  12   a ,  12   b ,  12   c  slidably engaging the third slot  42  of the third connector  40  of another adjacent one of the planar panels  12   a ,  12   b ,  12   c . The second blind end  38  of the second slot  36  abuts against the third blind end  44  of the third slot  42  to mechanically interconnect the first, second and third planar panels  12   a ,  12   b ,  12   c  with respect to one another, such that a first joint is formed at the intersection of each planar panel and an adjacent planar panel. 
     As best seen in  FIGS. 1A-1C , the kit can include a surface area  52  bounded by a first side  14 , a second side  20 , and a third side  24 . The surface area  52  can be formed with an optional lattice structure  54  defining a plurality of apertures  56 . The surface area  52  can be bound and defined by a fourth side, a fifth side, or any number of other sides with straight portion, non-straight portions, or any combination thereof to define a peripheral edge of each planar panel. The lattice structure  54  can be disposed within the surface area and can define a plurality of apertures  56 . The lattice structure can be webbing, a plurality of cross-hatched members, and any combination of generally elongated members extending between at least the first side, the second side, and the third side and define a plurality of apertures  56 . The planar panel can be formed with a generally planar solid body extending between at least the first side, the second side, and the third side without any apertures. A void or aperture can be defined and bound by at least the first side, the second side, and the third side. The lattice structure  54  can provide aesthetic value, structural support, and other desired characteristics to each planar panel. 
     The kit can include a first planar panel  12   a  and a second planar panel  12   b . The second connector  34  of the first planar panel  12   a  can be connectable to the third connector  40  of the second planar panel  12   b  to form a first slidable joint. When assembled in a different configuration, the first connector  28  of the first planar panel  12   a  can be connectable to the first connector  28  of the second planar panel  12   b  to form a second slidable joint. 
     One of ordinary skill in the art will appreciate that while the first and second slidable joints do not require additional fastening or connecting means to ensure that first, second, or third planar panels remain operatively engaged to one another, the inclusion of additional connecting means, although not required, remains within the spirit and scope of the present invention. 
     The kit can further include a first, a second and a third planar panel  12   a ,  12   b , and  12   c . Each planar panel can have at least three sides. The first side  14  can include a straight edge with a first end  16  and a second end  18 . The second side  20  can be connected to the first end  16  and extend from the first side  14  at a first predetermined angle  22 . The third side  24  can be connected to the second end  18  and extend from the first side  14  at a second predetermined angle  26 . 
     The kit can further include a first connector  28  integrally formed with the first side  14 . The first connector  28  can define a first slot  30  between the first side  14  and the first connector  28 . The first slot  30  can have a first blind end  32  substantially located at the midpoint of the first side  14 . The first slot  20  can be defined to be extending substantially parallel to the first side  14 . 
     The kit can further include a second connector  34  integrally formed with the second side  20 . The second connector  34  can define a second slot  36  having a second blind end  38  between the second side  20  and the second connector  34 . The second slot  36  can be defined to be extending substantially parallel to the second side  20 . 
     The kit can further include a third connector  40  integrally formed with the third side  24  defining a third slot  42 . The third slot  42  can have a third blind end  44  between the third side  24  and the third connector  40 . The third slot  42  can be defined to be extending substantially parallel to the third side  24 . 
     Referring to  FIGS. 3A-3B and 4A-4C  a planar panel  12  can form a regular equilateral panel from line A-B, A-D, and B-D. The planar panel  12  can include a first connector  28 , second connector  34 , and third connector  40 . Three panels of identical dimensions formed by lines AB, AD, and BD can make up three panels  12   a ,  12   b , and  12   c  that can be assembled into a module  62  and further assembled into a larger superstructure  80 , as seen in  FIG. 8 , in the same manner as described with respect to the irregular panels of  FIGS. 1A-1C and 10A-10B . Alternatively, three panels of non-identical dimensions formed by lines AB, AD, and BD can make up three panels  12   a ,  12   b , and  12   c  that can be assembled into a module  62  and further assembled into a larger superstructure  80 , as seen in  FIG. 8 , in the same manner as described with respect to the irregular panels of  FIGS. 1A-1C and 10A-10B . 
     The kit can include a first planar panel  12   a  and a second planar panel  12   b , and a third planar panel  12   c , each planar panel  12   a ,  12   b ,  12   c  with first, second, and third connectors slots and blind ends respectively. As best seen in  FIG. 4A , the second connector  34  (vertex A) and third connector  40  (vertex B) of each adjacent planar panel  12   a ,  12   b , and  12   c  can mechanically engage with one another to define a three dimensional geometric shape  62 , wherein the second slot of the second connector  34  of the first planar panel  12   a  operably engages with the third slot of the third connector  40  of the second planar panel  12   b  to define a first sliding joint. The second connector  34  and third connector  40  of each planar panel  12   a ,  12   b ,  12   c  can mechanically engage with one another to define a three dimensional geometric shape  62 . The three dimensional geometric shape  62  is defined with the second slot of the second connector  34  of one of the planar panels  12   a ,  12   b ,  12   c  slidably engaging the third slot of the third connector  40  of another adjacent one of the planar panels  12   a ,  12   b , and  12   c . The first connector  28  of each planar panel  12   a ,  12   b , and  12   c  can mechanically engage with other first connectors  28  of an additional three dimensional geometric shape  62 . 
     Referring to  FIGS. 5A and 5B , a planar panel  12  can form a regular equilateral triangle from line A-B, A-D, and B-D where the first  28 , second  34 , and third connectors  40  can have a curved edge or an edge defining a compound curve. A first, second, and third planar panel  12   a ,  12   b , and  12   c  can be joined in a similar fashion as described according to  FIGS. 4A, 4B, and 4C  to define a three dimensional geometric shape  62 . 
     Referring now to  FIGS. 1A and 6 , the second connector  34  and third connector  40  of each planar panel  12   a ,  12   b ,  12   c  can mechanically engage with one another to define a three dimensional geometric shape. The second slot  36  of the second connector  34  (vertex B) of the first planar panel  12   a  can slidably engage the third slot  42  of the third connector  40  (vertex B) of the second planar panel  12   b . The second slot  36  of the second connector  34  (vertex C) of the second planar panel  12   b  can slidably engage the third slot  42  of the third connector  40  (vertex C) of the third planar panel  12   c . The second slot  36  of the second connector  34  (vertex A) of the third planar panel  12   c  can slidably engage the third slot  42  of the third connector  40  (vertex A) of the first planar panel  12   a . The second blind ends  38  of each of the second slots  36  can be brought into a position to abut the third blind end  44  of the third slot  42  to mechanically interconnect the first planar panel  12   a , the second planar panel  12   b , and the third planar panel  12   c  with respect to one another. A first joint is formed and defined at the intersection of each planar panel and an adjacent planar panel as best seen in  FIG. 2A . In other words, a first joint can be formed with the second slot  36  of each of the first, second, and third planar panels  12   a ,  12   b ,  12   c  operatively engaging with the third slot  42  of another one of the first, second and third planar panels  12   a ,  12   b ,  12   c  to define at least one substantially tetrahedron-shaped  62  assembled modular sub-structure. 
     Referring to  FIGS. 1A and 7 , the kit can further include five irregular module sub-structures  62   a ,  62   b ,  62   c ,  62   d , and  62   e . A second joint can be defined by two first slots  30  of each of the irregular module sub-structures slidably engaging with two first slots  30  of adjacent irregular module sub-structures as best shown in  FIG. 10B . The first blind ends  32  can abut one another to form a substantially pentagon-shaped assembled modular sub-structure  74 . The second sliding joint can be formed by slidably engaging the first connector  28  and first slot  30  of a first irregular module sub-structure  62   a  with the first connector  28  and first slot  30  of an adjacent second irregular module sub-structure  62   b ,  62   c ,  62   d , and  62   e . The first blind end  32  of the first slot  30  of the first irregular module sub-structure  62   a  can abut the first blind end  32  of the first slot  30  of the second irregular module sub-structure  62   b ,  62   c ,  6   d , and  62   e . The first slot  30  of one irregular tetrahedron-shaped assembled module sub-structure can be substantially filled with the first connector  28  of another irregular tetrahedron-shaped assembled module sub-structure. In the assembled relationship, a portion of the first connector  28  of one sub-structure can overlie the adjacent first connector  28  of another sub-structure. In this way, the first module structure  62   a  and the second through fifth module structures  62   b ,  62   c ,  62   d ,  62   e  are connectable with respect to one another to form an assembled pentagonal shaped structure  74 . 
     Referring to  FIG. 8 , the at least one assembled pentagonal shaped structure  74   a  can further include a plurality of pentagonal shaped structures  74   a  and  74   b  mechanically interconnected to one another to form a larger modular structure  80 . The at least one assembled larger modular structure  80  can be at least one of a substantially dome shaped structure and a substantially egg shaped structure enclosing an open space or a cavity (not shown). Alternatively, the at least one assembled larger modular structure  80  can be of virtually any three-dimensional shape as desired with a cavity being optionally defined. 
     The kit can further include a first, a second, and a third planar panel  12   a ,  12   b , and  12   c . Each planar panel can have at least three sides. A kit  10  for building a structural shape can include a planar panel  12 . The planar panel  12  can have at least three sides. The first side  14  can include a straight edge with a first end  16  and a second end  18 . The second side  20  can be connected to the first end  16  and extend from the first side  14  at a first predetermined angle  22 . The third side  24  can be connected to the second end  16  and extend from the first side  14  at a second predetermined angle  26 . 
     The kit can further include a first connector  28  integrally formed with the first side  14  and defining a first slot  30  between the first side  14  and the first connector  28 . The first slot  30  can have a first blind end  32  substantially located at the midpoint of the first side  14 . The first slot  20  can be defined to be substantially parallel to the first side  14 . 
     The kit can further include a second connector  34  integrally formed with the second side  20  defining a second slot  36 . The second slot  36  can have a second blind end  38  between the second side  20  and the second connector  34 . The second slot  36  can be defined to be substantially parallel to the second side  20 . 
     The kit can further include a third connector  40  integrally formed with the third side  24  defining a third slot  42 . The third slot  40  can have a third blind end  44  between the third side  24  and the third connector  40 . The third slot  42  can be defined to be substantially parallel to the third side  24 . 
     The second connector  34  and third connector  40  of each planar panel  12   a ,  12   b ,  12   c  can mechanically engage with one another to define a three dimensional geometric shape, where the second slot  36  defined by the second connector  34  of the first planar panel  12   a  slidably engages the third slot  42  defined by the third connector  40  of the second planar panel  12   b  to define a first joint. The second slot  36  defined by the second connector  34  of the second planar panel  12   b  slidably engages the third slot  42  defined by the third connector  40  of the third planar panel  12   c  to define another first joint. The second slot  36  defined by the second connector  34  of the third planar panel  12   c  slidably engages the third slot  42  defined by the third connector  40  of the first planar panel  12   a  to define another first joint. The second blind ends  38  of each of the second slots  36  can abut the third blind end  44  of the third slot  42  to mechanically interconnect the first planar panel  12   a , the second planar panel  12   b , and the third planar panel  12   c  with respect to one another through three first joints. The first joint can be defined at the intersection of each planar panel and an adjacent planar panel. In other words, the first joint can be formed with the second slot  36  of each of the first, second, and third planar panels  12   a ,  12   b ,  12   c  operatively engaging with a corresponding third slot  42  of another one of the first, second and third planar panels  12   a ,  12   b ,  12   c  to define at least one regular or irregular substantially tetrahedron-shaped  62  assembled modular sub-structure. 
     The at least one irregular module structure  62  can further include first  62   a , second  62   b , third  62   c , fourth  62   d , and fifth  62   e  module structures  62 . The first connectors  28  of the first through fifth module sub-structures can mechanically engage one another to define a second joint. One of the first blind ends  32  of one of the first slots  30  of the first sub-structure can abut one of the first blind ends  32  of another one of the first slots  30  of an adjacent sub-structure. The first irregular module structure  62   a  and the adjacent irregular module structures  62   b - 62   e  are connectable with respect to one another through ten second joints to form at least one substantially pentagonal shaped structure  74 . 
     The at least one substantially pentagonal shaped structure  74  can further include a first  74   a  and a second  74   b  substantially pentagonal shaped structures  74 . The first slot  28  defined by the first connector  30  of the first substantially pentagonal shaped structure  74   a  can slidably engage the first slot  30  defined by the first connector  28  of the second substantially pentagonal shaped structure  74   a  to define a second joint. The first blind end  32  of each of the first slots  28  can abut the first blind end  32  of the first slot  30  to mechanically interconnect the first substantially pentagonal shaped structure  74   a  and second substantially pentagonal shaped structure  74   b  to form at least one modular superstructure  80 . 
     The at least one modular superstructure  80  can be substantially dome or egg shaped. Alternatively, the at least one modular structure  80  can be of virtually any three-dimensional shape as desired. A superstructure or modular structure  80  can be formed by using planar panels  12  of different dimension from the straight first edge or side  14  to the opposite edge or side while constructing sub-structures or modules  62 ,  74  for use along a particular horizontal row located at a different particular elevation of the superstructure being built. The at least one modular superstructure  80  can be substantially rectangular, square, trapezoidal, spherical, pyramidal, rhomboidal, or of any other suitable shape and dimension. It should be recognized by those skilled in the art that using different dimension planar panel  12  and different edge boundaries between the second and third sides  20 ,  24  can provide varying dimension building blocks or sub-structures and different aesthetic appearances as desired. 
     One of ordinary skill in the art will appreciate that in use and in practice, the individual planar panels  12 , the individual substantially tetrahedron shaped module sub-structures  62 , the individual substantially pentagon shaped module structures  74 , and the individual modular superstructures  80  can provide a myriad of applications and uses. The invention disclosed herein can provide application and use as an aesthetic structure, a load-bearing structure, or a number of other situations. Additionally, one of ordinary skill in the art will appreciate the ease and simplicity of packing individual panels  12  onto another for ease of transport or shipping prior to the construction of a structure, or after deconstruction of a structure. 
     Referring to  FIGS. 2A-2C, and 9A-9C , the tetrahedron structure  62 ,  62   a ,  62   b , and  62   c  is a reference shape for designing the panels  12  and module  80 . The tetrahedron structure  62   a ,  62   b , and  62   c  is a three sided pyramid and does not have to be regular or symmetrical in shape. The design of each module is based on the location of vertices in a tetrahedral arrangement. Vertices (also known as corners) are the points of the triangular faces of each panel that adjoin to form a tetrahedron. There can be four vertices A, B, C, and D in a tetrahedron  62 ,  62   a ,  62   b , and  62   c . In other words, the tetrahedron is made out of three planar panels that connect at and share vertices A, B, C, and D with one another. The vertices and edges of the panels  12  define the boundaries between the tetrahedron. Three of the vertices, A, B, and C, will always lie in the same plane, i.e. the vertices define a flat plane with the three points A, B, C. The forth vertex D is located somewhere else in space, anywhere but on the plane defined by the vertices A, B, C. The plane defined by the vertices A, B, C is the open face shown in  FIGS. 2A-2C  of the assembled tetrahedron, in that there is no planar panel component. The interlocking planar panels can lay oriented along the plane of the other three panels in the tetrahedron: A-C-D; C-B-D; and A-B-D. 
     Each planar panel  12   a ,  12   b , and  12   c  is flush with the adjacent planar panel  12   a ,  12   b , and  12   c  in the same plane of the slot geometry, or tetrahedral reference lines, which define how the panels  12   a ,  12   b , and  12   c  relate and connect to each other. All of the connectors  28 ,  34 , and  40  in the panels  12   a ,  12   b , and  12   c  are related to each other through the intersection of the three panels relating to this tetrahedral slotting geometry. The slots  30 ,  36 ,  42  have a connector  28 ,  34 , and  40  touching the outside of the adjacent panel  12   a ,  12   b , and  12   c  and the dimensions of each slot  30 ,  36 ,  42  are such that they can hold the width of another planar panel. The reference lines define the angle at which the slots are arranged, with one connector connectors  28 ,  34 , and  40  touching the reference line and other offset outside to accommodate the thickness of the panel. The slots  30 ,  36 ,  42  lie parallel to the respective reference line that connects vertex D to vertices A, B, C. 
     It should be noted that one surface defining an edge of the slot  30 ,  36 ,  42  is located on a reference line relating the vertices, while the slot is not centered to the reference line. This allows the panels  12  to bypass each other in forming a stable structure  62 ,  74 ,  80 . The inside surface of a panel  12 , when the panel is assembled to other panels to form part of the tetrahedron module, will be flush with the plane of that face. Edges of each panel touch in places other than the slot in order to hold the assembly of panels together, so the individual slots and connectors are not taking all the weight. The connectors  28 ,  34 ,  40  can be flared at the non-blind end to ease joining of steep angles or more rigid materials. It should further be noted that a plurality of connectors  28 ,  34 ,  40  can be provided along the first edge  14  if desired, as long as a length of the edge  14  is divided equidistantly with lengths between the blind ends of connectors  28 ,  34 ,  40 . 
     Referring to  FIGS. 9A, 9B, 10A, and 10B , modules  62  or superstructures  80  can be either regular or irregular, and can be fit together to form any triangular network as long as the vertices are contiguous. In other words, where the panels share edges and vertices, such that mapping the A, B, C vertices of the modules to the vertices of the panels in the network of the desired form, means the first connector in each module can be congruent with respects to vertices, edges, and connectors, so the shapes are an adjoined network of the open face at panel A, B, C. The modules allow construction of platonic solid shapes, such as the tetrahedron  62  which is the basis for the three panel module and the building of larger shapes with a plurality of tetrahedron modules, like a dodecahedron. 
     If the surface of a desired shape can be divided into adjoining panels of any dimension, as long as the vertices correspond to each other, the surface of the shape can be recreated with interlocking tetrahedral modules  62   a ,  62   b ,  62   c . Adjoining modules do not have to be of the same dimensions. Adjoining modules only need to have the same length along the side where the adjoining modules touch and join together to form a larger structure. This means that irregular and regular tetrahedral modules of varied dimensions can be combined, if desired. 
     As should be recognized by those skilled in the art, this gives rise to use of the present invention, from kits with repeating panels to relevant contemporary digital fabrication techniques, where technology is used to create cut schedules for the manufacture and assembly of many unique pieces. Modules can be constructed from identical panels or dissimilar panels, from regular shapes and irregular shapes. The pentagon module superstructure is based on an assembly of five irregular tetrahedron modules. A hexagonal module can also be constructed from regular tetrahedron modules. A dodecahedron module is constructed from irregular shaped tetrahedron modules. 
     While the invention has been described in connection with what is presently considered to be the most practical embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiments but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims, which scope is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures as is permitted under the law.