Distance between successive tetrahedral voids in FCC What is the distance between successive tetrahedral voids in a FCC
crystal structure? 

The distance between a face centered atom and a tetrahedral void is $\sqrt{\frac{3a}{4}}$ if the cube's edge length is $a$. Now If I know the angle made, between the line joining a tetrahedral void and the face centered atom, and the successive tetrahedral void and face centered atom, I can find the distance.  But how do I calculate that distance since I don't know the angle.
As shown in figure, if we divide a FCC unit cell into 8 small cubes, then each small cube has 1 Tetrahedral void at its own body centre.
Thus, there are total 8 Tetrahedral voids in one unit cell.
It can also be seen from the figure that the nearest distance between two Tetrahedral voids is a/2.