It is often remarked that the packing density of proteins is high. To understand the concept of packing density in 3D, look at sphere packings with sphere centers on the cubic lattice and the face-centered cubic lattice. The concept of packing density is important not just to help visualize molecule in space, but the special lattices involved are often used in lattice models of proteins. It is also a highly controversial mathematical topic because of the Kepler conjecture . For more information, go to the Weisstein site .
Lattices are actually fairly simple as three dimensional patterns go.
They remain unchanged if you translate them in certain directions. They are really groups of translations. When you take more complex euclidean motions, you get more complex patterns. These can be important in the study of crystallography. Again it is best to start with 2D. People have studied infinitely repeating 2D patterns of symmetry for years.