Does this structure correspond to anything in nature (apart from oranges in supermarkets) ? Of course ! A stack of layers of types ABC.ABC... represents the ¶cubic close-packed CCP atomic structure of gold as determined by X-rays. Atoms lie on the corners of a cube, with additional atoms at the centers of each cube face: for that reason it is often called face centered cubic or FCC. Many simple metals have this FCC structure, whose symmetry is described as Fm-3m where F means Face-centered,m signifies a mirror-plane (there are two) and -3 tells us that there is a 3-fold symmetry axis (along the body diagonal) as well as inversion symmetry.
Actually there is another common form of close-packing, corresponding to layers with stacking AB.AB... or AC.AC... (these are equivalent). This is called ¶hexagonal close-packing HCP, and the competition between CCP and HCP is determined by longer range forces between the atoms. This is the structure of sodium at low temperatures. No, we can't transform sodium to gold by stacking the atoms differently ! For such simple materials, the different properties are mainly due to the differences between the sodium and gold atoms themselves.
The third common metallic structure is called ¶body-centered cubic BCC, and consists of a unit cube with atoms at its corners and center. The BCC structure is slightly less closely packed than FCC or HCP and is often the high temperature form of metals that are close-packed at lower temperatures. For example sodium changes from HCP to BCC above -237 degrees C ! The structure of iron (Fe) can be either CCP or BCC depending on its heat treatment, while metals such as chromium are always BCC.
Metals which are BCC are, like chromium, usually harder and less malleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the BCC structure. Note that there are other important mechanisms for hardening metals, and these involve introducing impurities or defects which also block slipping.
Hmm. That's all very well if we have only one kind of atom, but
what if we have two or more types of atom, such as sodium and chlorine
in common salt ? Here's a clue: when the big atoms pack together, they
still leave holes for the smaller atoms. Lets see how
this works for salt !