Apollonian spheres

Apollonian spheres refer to a concept in geometry involving the arrangement of circles or spheres such that they are mutually tangent, meaning they touch each other at points but do not intersect. Named after the ancient mathematician Apollonius of Perga, these spheres create intricate patterns. In three-dimensional space, for any three touching spheres, an infinite number of other spheres can fit perfectly into the gaps between them, leading to fascinating configurations. This concept is not only of mathematical interest but also finds applications in various fields, including physics, engineering, and computer graphics.