Uploaded August 2012 | Updated September 2026, 2 weeks ago
The lattice of the A_3 root system (A_3 lattice for short) goes by many names: it is also the D_3 lattice, the (vertex arrangement) of the tetrahedral-octahedral honeycomb, the face-centered cubic (or close-packed cubic) crystal system, or A-B-C dense sphere packing system. It consists of three alternating layers of plane hexagonal arrangements, or equivalently, two alternating layers of plane square arrangements; and it defines tetrahedral and octahedral cells. This video shows a set of thusly arranged spheres (323 of them, the closest neighbors of a central sphere) being rotated by one full turn.
The lattice of the A_3 root system (A_3 lattice for short) goes by many names: it is also the D_3 lattice, the (vertex arrangement) of the tetrahedral-octahedral honeycomb, the face-centered cubic (or close-packed cubic) crystal system, or A-B-C dense sphere packing system. It consists of three alternating layers of plane hexagonal arrangements, or equivalently, two alternating layers of plane square arrangements; and it defines tetrahedral and octahedral cells. This video shows a set of thusly arranged spheres (323 of them, the closest neighbors of a central sphere) being rotated by one full turn.
