Not sure I understand the question fully, but here goes. If you heat a hexagonal honeycomb it becomes liquid. At that point the maximum volume can be contained in the minimum surface area (sphere). This happens because the wax is liquid and free to move. In crystals the crystal is solid and the molecules arrange themselves in the most stable form which is where their intermolecular forces are maximized. That is a repeating unit of some shape that forms and is locked in place as the molecules are not free to move.
Crystal is a solid with symmetrical repetition of atoms or molecules. The representation of a crystal is a unit cell, and this representation must be modeled by certain rules. One of the rules of unit cells is that they must be repeated along the space, and must not leave any empty space.
Spheres repeated along some space leaves empty spaces, and is not suited to represent a solid. Hexagons repeated along a space does leave empty spaces.
It's the concept of unit cell. Imagine a solid with billions of atoms or molecules. Study this system would be impossible due to the amount of atoms or molecules. So, unit cell is an abstract structure, with only few atoms, used to describe that whole system composed by billions of atoms. It's like unit cell was a small part of that solid. Then, from the unit cell, you can "construct" the whole solid, by repeating the unit cell along all the space. And when you repeat it, unit cells must "touch" each other side by side.
Imagine the space as a wall, in which you put blocks to completely fill the wall. If you use a square block, you fill the wall without leave any empty space between the blocks. As well as with "hexagonal" block, like a honeycomb, the wall would be filled with no empty space between them. But sphere blocks put together does leve empty spaces between them, they do not fill the wall completely.