Mircea Draghicescu

The internal structure of this sphere is based on a hierarchy of polyhedra that starts with the rectification of some "seed" (here a tetrahedron) and continues with each subsequent polyhedron being the rectification of the preceding one. There are three concentric layers: an octahedron inside a cuboctahedron inside a rhombicuboctahedron. All vertices have degree four and each cross-shaped piece corresponds to a vertex and its adjacent half-edges. Each piece also corresponds to an edge on the layer below, physically joining two pieces on this layer. In principle, this construct can be continued with more layers; in this work, 48 disks, corresponding to the vertices of a rectified rhombicuboctahedron, join the pieces on the outer layer.