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NonCommercial-ShareAlike 4.0 International

https://creativecommons.org/licenses/by-nc-sa/4.0/

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

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

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.

We will now unhighlight it and ignore it.

Counter:

No. of unit cells each lattice point belongs to:

Green:2

Red:2

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

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.

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.