Geometric systems for building 3-d structures

Abstract

Geometric systems including 2-D building elements configured to connect together for building 3-D structures, the of 2-D building elements each have a body that is at least: a central main body, tabs extended away from the central main body, and notches, one of the notches being disposed between each of the tabs and the central main body are described. The notches are oriented to form an underlying polygon of the central main body, and a width of each of the tabs is no greater than one half a length of one side of the underlying polygon. In some examples, where each of the tabs is comprised of a substantially rigid material, the width of the tab is no greater than one third the length of one side of the underlying polygon. In other examples, where each of the tabs is comprised of a substantially flexible material, the width of the tab is no less than one third the length of one side of the underlying polygon.

1 . A geometric system for building 3-D structures, comprising:
 a plurality of 2-D building elements configured to connect together for building 3-D structures, each of the plurality of 2-D building elements having a body that is at least:
 a central main body, 
 a plurality of tabs at least partially continuous with and extended away from the central main body, and 
 a plurality of notches, one of the plurality of notches being disposed between each of the plurality of tabs and the central main body, 
   wherein the plurality of building elements is configured to fit together at respective notches of each building element to form a 3-D structure, and   wherein each of the plurality of notches is oriented relative to adjacent notches to form an underlying polygon of the central main body, a width of each of the plurality of tabs being no greater than one half a length of one side of the underlying polygon.   
     
     
         2 . The geometric system of  claim 1 , wherein a length of each of the plurality of notches is no greater than one half the width of each of the plurality of tabs. 
     
     
         3 . The geometric system of  claim 1 , wherein each of the plurality of 2-D building elements is comprised of a substantially rigid material. 
     
     
         4 . The geometric system of  claim 3 , wherein the width of each of the plurality of tabs is no greater than one third the length of one side of the underlying polygon. 
     
     
         5 . The geometric system of  claim 1 , wherein each of the plurality of 2-D building elements is comprised of a substantially flexible material. 
     
     
         6 . The geometric system of  claim 5 , wherein the width of each of the plurality of tabs is no less than one third the length of one side of the underlying polygon. 
     
     
         7 . The geometric system of  claim 1 , wherein the plurality of 2-D building elements are comprised of one or more of ethylene vinyl acetate, poster board, laminated paper, wood veneer, acrylic, and sisal. 
     
     
         8 . The geometric system of  claim 1 , wherein the plurality of building elements comprises at least a first building element and a second building element, and
 wherein the plurality of notches are rectilinear for the first building element and non-rectilinear for the second building element, opposing longitudinal sides of the plurality rectilinear notches comprising two straight lines and opposing longitudinal sides of the plurality of non-rectilinear notches comprising a straight line and a curved line.   
     
     
         9 . The geometric system of  claim 8 , wherein the second building element is comprised of a rigid material. 
     
     
         10 . The geometric system of  claim 1 , wherein each the plurality of notches is of equal dimensions relative to others of the plurality of notches, and each of the plurality of tabs is of equal dimensions relative to others of the plurality of tabs. 
     
     
         11 . The geometric system of  claim 1 , wherein the distance from each of the plurality of notches to the center of the building elements is selected such that the plurality of building elements to form a 3-D structure having faces that are equiangular and equilateral when interconnected. 
     
     
         12 . A geometric system for building 3-D structures from a plurality of 2-D building elements, comprising:
 a plurality of 2-D building elements configured to connect together for building 3-D structures, each of the plurality of 2-D building elements having a main body which is at least:
 a central main body, 
 a plurality of elongate projections continuous with and extended away from the central main body, and 
 a plurality of notches, one of the plurality of notches being disposed in each of the plurality of elongate projections, portions of the plurality of elongate projections extended beyond the plurality of notches being a plurality of tabs, 
   wherein the plurality of building elements is configured to fit together at respective notches of each building element to form a polyhedron structure.   
     
     
         13 . The geometric system of  claim 12 , wherein each of the plurality of notches is oriented relative to adjacent notches to form an underlying polygon of the main body, each of the plurality of tabs having a width that is no greater than one half a length of one side of the underlying polygon. 
     
     
         14 . The geometric system of  claim 13 , wherein each of the plurality of 2-D building elements is comprised of a substantially rigid material, and a width of each of the plurality of tabs is no greater than one third a length of one side of the underlying polygon. 
     
     
         15 . The geometric system of  claim 13 , wherein each the plurality of 2-D building elements is comprised of a substantially flexible material, and a width of each of the plurality of tabs is no greater than one half a length of one side of the underlying polygon. 
     
     
         16 . The geometric system of  claim 15 , wherein a width of each of the plurality of tabs is no less than one third a length of one side of the underlying polygon. 
     
     
         17 . The geometric system of  claim 12 , wherein a length of each of the plurality of notches is no greater than one half a width of each of the plurality of tabs. 
     
     
         18 . A geometric system for building 3-D structures, comprising:
 a plurality of 2-D building elements configured to connect together for building 3-D structures, each of the plurality of 2-D building elements having a main body that is at least:
 a central main body, 
 a plurality of tabs at least partially continuous with and extended away from the central main body, and 
 a plurality of notches, one of the plurality of notches being disposed between each of the plurality of tabs and the central main body, 
   wherein the plurality of building elements are configured to fit together at their respective notches to form a 3-D structure,   wherein each of the plurality of notches is oriented relative to adjacent notches to form an underlying polygon of the main body, each of the plurality of tabs having a width that is no greater than one half a length of one side of the underlying polygon, and   wherein a length of each of the plurality of notches is no greater than one half the width of each of the plurality of tabs.   
     
     
         19 . The geometric system of  claim 18 , wherein each of the plurality of 2-D building elements is comprised of a substantially flexible material, and a width of each of the plurality of tabs is no less than one third a length of one side of the underlying polygon. 
     
     
         20 . The geometric system of  claim 18 , wherein each of the plurality of 2-D building elements is comprised of a substantially rigid material, and the width of each of the plurality of tabs is no greater than one third the length of one side of the underlying polygon.