SuperCube Spheres, 2017

The SuperCube Spheres report generalizes the SuperCubeSphere system for bigger polyhedra. It generalizes 3- and 5-cube clusters by adding pairs of cubes to give the bigger icosahedron and dodecahedron. It discusses how to extend the edges with a periodicity in a superstructure made up of interlocking pairs that can be extended. The dihedral angles are created in the base cluster, the linear extension is created in the elements. It tests the geometric consistency of the scaling law between different sizes. What kind of polyhedra are created by systematic extension? What is the relationship of the golden ratio at different scales? The spherical form adapts to generate larger forms while preserving the logic of interlocking modular forms and the principles of icosahedral symmetry used in the SuperCubeSphere.