Calculate the third and fourth nearest neighbours in bcc My textbook has given data for third and fourth nearest neighbours to be 12 and 8 with distances $\sqrt{2}a$ and $\frac{\sqrt{11}a}{2}$.

I have been able to calculate for  the first and second nearest neighbour but it has become difficult to visualise for the other two to calculate. Can you help me with hints on how to proceed preferably with a diagram.
With $\sqrt3\over2$ being that close to $1$, BCC packing is better not looked at in terms of coordination spheres. But if you insist...

Say you are sitting in the center of a cell. Then:


Your first neighbours are at the corners of the same cell.
Second neighbours are at the centers of the nearest adjacent cells.
Third neighbours: centers of the next adjacent cells (those which share two corners with your cell).
Fourth neighbours: far corners of the nearest adjacent cells.


On a side note, there are more than just 8 of the latter.