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.