In three dimensions, three-dimensional objects may be arranged in a considerably larger number of ways, and many of these are exhibited in crystal forms. Again, each possible arrangement is achieved by a combination of simple, basic operations. These include translation, rotation, screw-rotation, mirror, inversion, inversion-rotation, and glide-reflection. The total number of possible ways of arranging copies of the same object in 3D-space can be shown to total 230. These are the `Space Groups' familiar to crystallographers. They are enumerated and detailed in The International Tables.
Now, proteins are chiral objects, and cannot be mirror-inverted whilst remaining the same. Their mirror reflection is DIFFERENT. Thus, many of these arrangements are actually precluded. In fact, proteins may only adopt 65 of the 230 possible 3D space groups. Many of these are observed when we crystallise proteins.
In the case of naturally occurring multimers of proteins, other constraints occur which limit the possible arrangements. We are speaking here of individual assemblies of monomer units, creating (usually soluble) complexes which exhibit internal symmetry.
Thus, the monomers must associate with van der Waals contact interfaces between the sub-units of the assembly. But, the sub-units cannot intersect. They may interpenetrate only in so far as there exist corresponding `knobs' and `holes'.
This