 Apollonian sphere packing

Apollonian sphere packing is a fascinating and complex concept in geometry and number theory that involves the arrangement of spheres in three-dimensional space. The defining feature of Apollonian sphere packing is that it consists of an arrangement of spheres where each sphere is tangent to three others. Here’s a more detailed breakdown of the concept: ### Construction: 1. **Initial Configuration**: The process begins with three mutually tangent spheres. This creates a triangle of points where each sphere touches the others.