The pictures below depict limit sets of groups generated by sphere inversions in 3d space. They're similar in spirit to the 2d limit sets explored in this series. The sphere inversions are chosen in a very particular way, pioneered by Vladimir Bulatov. There are two sets of sphere inversions, each located at the vertice of a regular polyhedron and of its dual. For some tuned values of the polyhedra radii and of the sphere radii, the limit sets look like 3d generalisations of the Apolonian gasket. 

For each image we list the "outside" and "inside" polyhedra. The images are stereographic: look at the right image with your left eye, and vice versa to see the limit set in three dimensions.