Kepler conjectured that face center cubic packing
was the densest possible packing scenario, but could not prove this mathematically.
In 1611, Johannes Kepler proposed that identical spheres can crowd together no more tightly than oranges do in a grocer's stack, a formation called face-centered cubic packing
Two random packing approaches, pouring and raining, were compared to the face--centered cubic packing
Such an arrangement is known as face-centered cubic packing.
In the 19th century, Carl Friedrich Gauss proved that face-centered cubic packing is the densest arrangement in which the centers of the spheres form a regular lattice.
The densest known packing in three dimensions, called the face-centered cubic packing
, is familiar to anyone who has seen neat piles of oranges at fruit stands.