A unit cell has several interstitial voids $($or spaces or sites$).$ There are two types of interstitial voids in FCC and BCC cells, namely, octahedral and tetrahedral. However, the octahedral and tetrahedral voids in BCC are not regularly shaped but distorted.

$($a$)$ How many$$distorted$$ octahedral and tetrahedral voids are there in a BCC cell?

$($b$)$ The centre of one of the tetrahedral voids in a BCC unit cell is located at $(,(1)/(2),0).$

$($i$)$ Name the Miller indices for the horizontal plane that passes through the centre of the void.

$($ii$)$ Calculate the radius of the largest atom that could fit in the void if the radius of the parent atom in this lattice is $0\mathrm{.}387$ nm$.$ Use a diagram to aid in your analysis.