There have long been results that show that the more dimensions you have, the less efficient the packing. Minkowski, Einstein's teacher, proved that the upper bound for sphere-packing density decreases exponentially as dimension increases. According to Scientific American,

Efficiently stacked oranges can fill about 74% of three-dimensional space. The sphere-packing problem has not been solved yet in four dimensions, but in eight dimensions, Viazovska showed that the densest packing fills about 25% of space, and in 24 dimensions, the best packing fills only 0.1% of space.

I find this very surprising.