Means and methods for construction and use of geodesic rhombic triacontahedron

Abstract

A structural system comprising the symmetrical interpenetration of an icosahedron and dodecahedron, further articulated to form a rhombic triacontahedron with each rhombus subdivided by two diagonals at its midpoint. The vertices of the original icosahedron and dodecahedron, and the midpoints of the rhombi, are projected such that a single circumscribed sphere would touch or nearly touch all three sets of resulting vertices. This geometry may used to create a hemispheric geodesic dome. Alternatively, this dome may be subdivided along the hemisphere's great circle segments into two half domes or four quarter domes. Rectangular structural elements may be inserted between the half or quarter domes to increase dome area without increasing dome height and to provide other advantages. The basic triangular components of the disclosed structure may be cut with minimal waste from conventional rectangular construction material such as Structural Insulated Panels. These basic triangular components may be connected with a living hinge.

1 . A building structure comprising a plurality of two sets of near right angle component triangles, with each set a mirror image of the other, such that the vertices of the structure are all of equal radial distance from the center of the structure, thus creating a structural approximation of a hemisphere with great circle segments crossing at the apex of the hemisphere.  
   
   
       2 . The building structure of  claim 1  wherein the vertices correspond to a subdivided rhombic triacontahedron such that vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are projected so that all three resulting sets of vertices are of equal radial distance from the center of the structure.  
   
   
       3 . The building structure of  claim 2  wherein the vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are of unequal radial distance from the center of the structure but are close enough to equal distance to produce near right angle component triangles which can be cut efficiently (less than 15% material cutting waste) from rectilinear building materials.  
   
   
       4 . The building structure of  claim 2  wherein the vertices of the original icosahedron, vertices of the original dodecahedron, and the midpoints of the rhombic diagonals are of unequal radial distance from the center of the structure but are close enough to equal distance to produce a close approximation of a hemisphere with great circle segments crossing at the apex of the hemisphere.  
   
   
       5 . The building structure of  claim 3  wherein the intersection points of the rhombi diagonals are projected to a radial length between the radius length of the icosahedron and the radius length of the dodecahedron.  
   
   
       6 . The hemisphere structure of  claim 2  subdivided into two half domes along either of the hemisphere's great circle segments.  
   
   
       7 . The two half domes of  claim 6  moved apart.  
   
   
       8 . The two half domes of  claim 7  with rectangular structural elements inserted between the two half domes.  
   
   
       9 . The two half domes of  claim 6  subdivided into four quarter domes along the remaining great circle segments of the original hemisphere.  
   
   
       10 . The four quarter domes of  claim 9  moved apart.  
   
   
       11 . The four quarter domes of  claim 10  with rectangular structural elements inserted between the four quarter domes.  
   
   
       12 . The building structure of  claim 1  constructed from structural insulated panels (SiPs).  
   
   
       13 . The building structure of  claim 1  comprising a basic spherical geometry comprising 62 vertices, 120 triangular faces and 180 edges, with all 120 triangular faces having the same angles and size, with 60 of the triangular faces being mirror images of the other 60 triangular faces.  
   
   
       14 . The building structure of  claim 12  wherein the triangular SIPs are beveled.  
   
   
       15 . The panels of  claim 14  wherein each edge of a panel has a different dihedral angle.  
   
   
       16 . The panels of  claim 15  wherein each edge of a triangular panel is approximately 2 degrees, 20 degrees and 30 degrees.  
   
   
       17 . The panels of  claim 16  connected together with a spline comprising a living hinge.  
   
   
       18 . The spline of  claim 17  fixed in three separate angles of approximately 2 degrees, 20 degrees, and 31 degrees.