A3/D3 Lattice
Its vertex arrangement represents an A3 lattice or D3 lattice. It is the 3-dimensional case of a simplectic honeycomb. Its Voronoi cell is a rhombic dodecahedron, the dual of the cuboctahedron vertex figure for the tet-oct honeycomb.
The D3+ packing can be constructed by the union of two D3 (or A3) lattices. The D3+ packing is only a lattice for even dimensions. The kissing number is 22=4, (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8).
- +
The A3* or D3* lattice (also called A34 or D34) can be constructed by the union of all four A3 lattices, and is identical to the vertex arrangement of the disphenoid tetrahedral honeycomb, dual honeycomb of the uniform bitruncated cubic honeycomb: It is also the body centered cubic, the union of two cubic honeycombs in dual positions.
- + + + = dual of = + .
The kissing number of the D3* lattice is 8 and its Voronoi tessellation is a bitruncated cubic honeycomb, containing all truncated octahedral Voronoi cells, .
Read more about this topic: Tetrahedral-octahedral Honeycomb