The BCC lattice is, you take the points (x,y,z) with integer coordinates, and then also adjoin a copy of that translated by (1/2, 1/2, 1/2). That is, the vertices of the usual grid of unit cubes, plus points at all the cube centers. Now suppose we change all the "cubes" to aXaXc "bricks" where a*a*c=1 (to keep the point-density at 2). This is a 1-parameter family of "tetragonal" lattices. Some interesting particular cases of it are: BCC: arises when a=c=1. Sphere packing volume-density = pi*sqrt(3)/8 = 0.6801747619 #nearest neighbors = 8 FCC: arises when a=0.8908987180, c=1.259921049, c/a=sqrt(2)=1.414213562. Sphere packing volume-density = pi/sqrt(18) = 0.7404804898 #nearest neighbors = 12 New(?) Lattice: arises when a=1.069913194, c=0.8735804647, c/a=sqrt(3/2)=1.224744871. Sphere packing volume-density = 2*pi/9 = 0.6981317011 #nearest neighbors = 10 -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)