The geodesic subdivision i.e. tessellation of the sphere derived from the spherical cube is little explored.
I wonder why?
Imagine a cube inscribed in a sphere. Now from the centre of the sphere project the edges of the cube on the circumsphere. The projected edges will follow great circle arcs i.e. geodesics. Each face of the cube can be divided into an orthogonal grid. Again projecting this grid from the centre of the sphere on the circumsphere will give a quadrilateral mesh with a geodesic pattern (all the lines follow great circle arcs). The number of divisions of the cube’s edge will give the frequency breakdown. The figures show a 6 frequency spherical cube.
This geodesic dome has a 4-fold symmetry, which makes it adaptable to plans with right angles, which is the norm.
Nowadays, when any imaginable configuration (sculpture) can be built, we should remind ourselves that the architectural language, for some 5000 years, is primarily based on the discipline of orthogonal ground plans! Also observe how the structures grow directly from the plans.
What is different and new?
Contemporary architects and engineers should ask: how much does their building weigh?
Of course, this design approach is not always appropriate.