the kepler conjecture is about sphere packing in three-dimensional euclidean space. it is named after johannes kepler (1571-1630) who first had this idea. kepler supposed that the ways to pack spheres of equal size that result in the packing with the highest density are face-centered cubic or hexagonal packings. those two things are crystal structures, meaning ways to put things together in a repeating pattern. these packings have a density of slightly over 74 percent, this means that they fill about 74 percent of space available.