# If the appearance of a crystal is octahedral crystals, can I deduce that the crystal structure is octahedral?

I have a physics problem in which I'm calculating the magnetic properties of "a paramagnetic salt like iron ammonium alum". I am half inclined to believe that I am supposed to treat the substance like a one-dimensional array of dipoles, but that's not actually correct - I would like to treat it like a volume, as it would be in practice. Since the first part of the question is about the strength of the magnetic field at a dipole due to its neighboring dipoles, I need to figure out how many neighboring dipoles there are. (This would be 2 for a one-dimensional array).

According to wikipedia, the appearance of iron ammonium alum is octahedral crystals. From this can I deduce that the crystal structure of the crystal is octahedral, and so each dipole has eight neighbors?

I'm not sure that would be correct, since a cubic crystal structure (such as that of NaCl) could also give rise to an octahedral appearance if the vertices of the cube are cleaved off to give flat faces (pictured in the top left drawing). However Wikipedia says the appearance of NaCl is cubic crystals.

Second of all, the vertex 2-coloring problem of the octahedron is not solvable (take any three vertices that make up a face, they cannot be colored in an alternating fashion) so an octahedral lattice might not be the lowest-energy configuration of a salt, unless it is made up of compounds of irregular shape and/or size. This could be the case for iron ammonium alum, but an irregular shape could also induce it to be cleaved as an octahedron even with a cubic crystal structure, in principle.

(This class hasn't gone over crystal structure at all nor do any of its prereqs teach that, so I don't believe that getting a full and complete answer to this question would be anything but scholarship)

• What do you mean by an octahedral crystal structure or an octahedral lattice? – Ivan Neretin Oct 27 at 8:43
• Octahedral crystal structure / lattice - the shape of the unit cell. I.e. if you place atoms at the vertices of an octahedron then the whole crystal structure is a tessellation of that shape. (Overlapping vertices are identified with each other as you tessellate the shape) – jcarpenter2 Oct 27 at 20:37
• You seem to be using your own definition, and a rather unique one at that. In my world, a unit cell is always a parallelepiped. – Ivan Neretin Oct 28 at 7:26
• Ah, I wasn't totally familiar with that. A parallelepiped captures most tessellations of actual crystal structures I would imagine, and it does capture this one (You can change it to your (and probably the accepted) definition of a unit cell by circumscribing an octahedron with a cube) but you could imagine structures it doesn't capture, like 3D-extended penrose tilings. – jcarpenter2 Oct 29 at 2:31
• Well, quasicrystals do exist, but they are not crystals, nor are they based on octahedra. – Ivan Neretin Oct 29 at 5:15