410.10 Omnitriangulation of Sixty Degrees

410.11 The closest packing of unit radius spheres always associates in omnitriangulations of 60 degrees, whether in planar or omnidirectional arrays. Six unit radius spheres pack most tightly around one sphere on a billiard table. Twelve unit radius spheres compact around one sphere in omnidirectional closest packing.

410.12 If we take three billiard balls on a flat table, we find that they compact beautifully into a triangle. If we arrange four of them on a billiard table in a square, they tend to be restless and roll around each other. If compacted into a condition of stability, the four form a 60-degree-angled diamond shape made of two stable triangles.