# How many tetrahedral and octahedral holes are there in a bcc unit cell?

When I tried to count, I found 24 tetrahedral holes (each formed by 2 body centers of 2 unit cells sharing a face and 2 vertices of the same edge of that face). As each hole is being shared by 2 unit cells, there are 12 holes per unit cell.

Also,I found 6 octahedral holes (6 at face centers being shard by 2 unit cells each and 12 at every edge center being shared by 4 unit cells each).

Generally I was taught that for $n$ packed spheres, there should be $2n$ tetrahedral holes. Does the analysis above mean that this rule doesn't apply here?

• Bcc isn't a close packed structure, so I don't think one should expect that the usual 1:1:2 ratio of sphere:octahedral hole:tetrahedral hole is fulfilled. As far as I can tell, your analysis leading to 6 octahedral and 12 tetrahedral per unit cell is correct (textbooks state this when describing the structure of α-AgI). However, these holes are slightly distorted from perfect octahedral/tetrahedral symmetry. – orthocresol Aug 27 '17 at 15:21

We have thus $6\times1/2 = 3$ distorted octahedral voids.