Coaxial Wireframe

This is a wireframe of a coaxial family of circles and its orthogonal family of circles on the sphere (also known as Apollonian circles). The circles are constructed as surfaces of revolution in such a way that each is the intersection of a sphere with a hollowed out cone.

What is remarkable about Apollonian circles like these is that every intersection of any two circle from one family with any circle from the other is at right angles. If you look closely you can see that the two families of