Hexagons are best for tiling 2D space in terms of perimeter vs area. What's best for 3D space? If you think of the bee-hive problem, you want to make 2D cells that divide the plane of honey into chunks of area while expending the least perimeter (since the perimeter of the cells is what takes up resources/effort). The solution ends up being the hexagonal tiling.
What is the analogous "tiling" for 3D space that's optimal in a similar sense? (more volume, less surface area)
And if possible, I'd like to know the general solution for $n$-D space.
To make the problem statement clear: assume that each "cell" has a volume of at most 1. With what polyhedron should you divide the cells to minimize the ratio of surface area to volume? For example, if you tile everything with hypercubes, the ratio would be $2n$, which probably isn't optimal.

This is known as the Kelvin problem; the best known (and conjectured optimal) solution is the Weaire–Phelan structure, but proving this is likely very very hard. I don't know what the best results in $n$ dimensions are, but I'd be shocked if they were solved for $n>3$.
                                              
