Geometric Systems for Building 3-D Structures

Abstract

Geometric systems for building 3-D structures from a plurality of 2-D building elements, including a first building element defining a first shape defined by edges with a first dimension, and a second building element defining a second shape incongruent to the first shape defined by edges with a second dimension incongruent to the first dimension. Further, each building element defines an imaginary circle having a center aligned with the center of the building element, and defines a plurality of notches positioned at and tangential to the circumference of the imaginary circle, where the plurality of building elements are configured to fit together at their respective notches to torn a 3-D structure. Geometric systems may include a first building element defining a first shape with a first contour, and a second building element defining a second shape incongruent to the first shape with a second contour incongruent to the first contour.

We Claim: 
     
         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, including:
 a first building element defining a first shape defined edges with a first dimension, and 
 a second building element defining a second shape incongruent to the first shape defined by edges with a second dimension incongruent to the first dimension; and 
   where each building element:
 defines an imaginary circle having a center aligned with the center of the building element, and 
 defines a plurality of notches disposed at the circumference of the imaginary circle and aligned tangentially to the imaginary circle; and 
   where the plurality of building elements, including the first building element and the second building element defining incongruent shapes, are configured to fit together at their respective notches to form a 3-D structure.   
     
     
         2 . The geometric system of  claim 1 , wherein the plurality of notches are rectilinear for the first building element and non-rectilinear for the second building element. 
     
     
         3 . The geometric system of  claim 1 , wherein the plurality of notches are arbitrarily rectilinear and non-rectilinear in shape for all of the interconnected 2-D building elements. 
     
     
         4 . The geometric system of  claim 1 , wherein the notches of each building element to be interconnected are of equal length. 
     
     
         5 . The geometric system of  claim 1 , wherein the distance from the notches to the center of the building elements is selected to cause the plurality of building elements to form a 3-D structure having faces that are equiangular and equilateral hen interconnected. 
     
     
         6 . The geometric system of  claim 1 , wherein the location of the notches in relation to the center of each building element is selected to cause the plurality of building elements to form a 3-D Platonic structure, a 3-D Johnson structure, or a 3-D Archimedean structure when interconnected. 
     
     
         7 . The geometric system of  claim 1 , wherein the 2-D building elements are made from ethylene vinyl acetate, poster board, or laminated paper. 
     
     
         8 . The geometric system of  claim 1 , wherein the 2-D building elements are made from wood veneer, acrylic, or sisal. 
     
     
         9 . The geometric system of  claim 1 , wherein the edges of the 2-D building elements are curvilinear. 
     
     
         10 . 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, including:
 a first building element defining a first shape defined by edges with a first contour, and 
 a second building element defining a second shape incongruent to the first shape defined by edges with a second contour incongruent to the first contour; and 
   where each building element:
 defines an imaginary circle having a center aligned with the center of the building element, and 
 defines a Plurality of notches disposed at the circumference of the imaginary circle and aligned tangentially to the imaginary circle; and 
   where the plurality of building elements, including the first building element and the second building element defining incongruent shapes, are configured to fit together at their respective notches to form a polyhedron structure.   
     
     
         11 . The geometric system of  claim 10 , wherein the plurality of notches are rectilinear for the first building element and non-rectilinear for the second building element. 
     
     
         12 . The geometric system of  claim 10 , wherein each 2-D building element is configured with at least three notches. 
     
     
         13 . The geometric system of  claim 10 , wherein the plurality of notches are non-rectilinear, allowing the interconnection of 2-D building elements that are made of various materials. 
     
     
         14 . The geometric system of  claim 10 , wherein the notches of each 2-D building element to be interconnected are of equal length. 
     
     
         15 . The geometric system of  claim 10 , wherein incongruent 2-D building elements are configured to have notches of the same length and to interconnect to form a 3-D Platonic polyhedron, a 3-D Johnson polyhedron, or a 3-D Archimedean polyhedron. 
     
     
         16 . The geometric system of  claim 10 , wherein the distance from the notches to the center of the building elements is selected to cause the plurality of building elements to form a 3-D structure having faces that are equiangular and equilateral when interconnected. 
     
     
         17 . The geometric system of  claim 10 , further comprising a plurality of edge tabs, the edge tabs being integrally formed with the edges of the 2-D building elements to form the notches. 
     
     
         18 . The geometric system of  claim 10 , wherein the contours of the 2-D building elements are curvilinear. 
     
     
         19 . The geometric system of  claim 10 , wherein the 2-D building elements are made from ethylene vinyl acetate, poster board, or laminated paper. 
     
     
         20 . The geometric system of  claim 10 , wherein the 2-D building elements are made from wood veneer, acrylic, or sisal.