Atoms touch along different directions in each structure. SC: atoms touch along edge, a = 2r. BCC: atoms touch along body diagonal (length = asqrt(3)), 4r = asqrt(3), so a = 4r/sqrt(3). FCC: atoms touch along face diagonal (length = asqrt(2)), 4r = asqrt(2), so a = 2*sqrt(2)*r. These are essential for converting between edge length and radius in density problems.