If the radius of the octahedral void is r and the radius of the atoms in the packing is R, derive relationship between r and R.

Explanation

Pythagoras theorem `AC^2=AB^2+BC^2(2R)^2=(R+r)^2+(R+r)^2`
`(2R)^2=2(R+r)^2(4R^2)/2=(R+r)^2,2R^2=(R+r)^2`
`(sqrt2R)^2=(R+r)^2,sqrt2R=(R+r),r=sqrt2R-R=(sqrt2-1)R=(1.414-1)=0.414R`