Close-packing of Equal Spheres - Lattice Generation

Lattice Generation

When forming any sphere-packing lattice, the first fact to notice is that whenever two spheres touch a straight line may be drawn from the center of one sphere to the center of the other intersecting the point of contact. The distance between the centers along the shortest path namely that straight line will therefore be r₁ + r₂ where r₁ is the radius of the first sphere and r₂ is the radius of the second. In close packing all of the spheres share a common radius, r. Therefore two centers would simply have a distance 2r.