# Cubic lattice: How corner atom of a cube is shared by 8 atoms? [closed]

Each atom is at the corner of a cube and 8 cubes meet at each corner. Therefore each atom is shared by 8 cubes.

But I can't imagine it in space, so please tell how I visualize it.

• As it stands, this is a geometry question. I assume this is related to a particular compound, probably ionic. Can you give an example compound? – Level River St Nov 8 '14 at 15:16
• you can consider any cubic compound. – Danish Firoz Nov 8 '14 at 15:19
• I've answered your question, based on the assumption you mean simple cubic lattice. Please include "cubic lattice" in the title so others can benefit from it. – Level River St Nov 8 '14 at 16:07
• I'm voting to close this question as off-topic because it's more of a geometry question. – Melanie Feb 27 '19 at 2:46

Surprisingly, this simple question does not seem to have been asked before. http://en.wikipedia.org/wiki/Bravais_lattice shows all the two dimensional Bravais lattices in extended form (but only the unit cell for the three dimensional ones.)

Here is the 2-dimensional image from wikipedia. As you can see in the simple square lattice, each sphere is a the corner of a square and 4 squares meet at each corner. Therefore each sphere is shared by 4 squares.

The simple cubic lattice is the same, except that the atoms are found at the corner of the cubic unit cell. Therefore each atom is shared by 8 unit cells. There are eight eighths (equal to one whole atom) in each unit cell.

I am not aware of any elements that crystallise in the simple cubic lattice. It is not energetically favoured because it is not spatially efficient. The more complex face-centred and body-centred lattices are preferred. Caesium Chloride, Bromide and Iodide form interpenetrating simple cubic lattices with the halide ion at the centre and the caesium ion at the corners of the unit cell (or vice versa depending on your viewpoint.)

Here are the relevant wikipedia links

http://en.wikipedia.org/wiki/Caesium_chloride

http://en.wikipedia.org/wiki/Caesium_bromide

http://en.wikipedia.org/wiki/Caesium_iodide

• I am not aware of any elements that crystallise in the simple cubic lattice. It is rare but Polonium actually crystallizes in a simple cubic structure (according to Wikipedia). – Philipp Nov 8 '14 at 16:36
• @Philipp that's bizarre, I didn't think that would be possible. It does say it's the only known example of a simple cubic structure on a single atom basis. The image on that article is actaully better than the one I have included. It also links to another page I didn't find before: en.wikipedia.org/wiki/Cubic_crystal_system – Level River St Nov 8 '14 at 19:18
• Simple cubic lattices are also in some compounds. Cesium chloride looks like it's bcc because of its eightfold coordination, but the nonequivalence of alternating cesium and chlorine atoms renders it actually simple cubic. – Oscar Lanzi Feb 26 '19 at 15:37

Here let me plot that for you in Diamond (Software):

• You might want to say "Diamond software" or some such thing, to avoid readers mistaking this for a (wrong) structure for a carbon allotrope. – Oscar Lanzi Feb 27 '19 at 12:21