Re-use of this resource is governed by a Creative Commons Attribution-
NonCommercial-ShareAlike 4.0 International
https://creativecommons.org/licenses/by-nc-sa/4.0/
creative commons DoITPoMS logo

Unit cell packing

Two lattice points are highlighted: a corner one in red and a face one in green

The counters show how many unit cells they're in as we pack the unit cells together
Counter:
No. of unit cells each lattice point belongs to:
Green:1
Red:1
Now the lattice point (green) in the face centre is shared between two unit cells and so contributes one 1/2 lattice point to the unit cell.

We will now unhighlight it and ignore it.
Counter:
No. of unit cells each lattice point belongs to:
Green:2
Red:2
Counter:
No. of unit cells each lattice point belongs to:

Red:4
Counter: Red:8

Each corner lattice point is shared between 8 unit cells and so contributes 1/8 of a lattice point to a unit cell.

Therefore, the 8 corner lattice points contribute
8 × 1/8 = 1 lattice point in total to our unit cell.