D6 Lattice
The vertex arrangement of the 6-demicubic honeycomb is the D6 lattice. The 60 vertices of the rectified 6-orthoplex vertex figure of the 6-demicubic honeycomb reflect the kissing number 60 of this lattice. The best known is 72, from the E6 lattice and the 222 honeycomb.
The D6+ lattice (also called D62) can be constructed by the union of two D6 lattices. This packing is only a lattice for even dimensions. The kissing number is 25=32 (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8).
- +
The D6* lattice (also called D64 and C62) can be constructed by the union of all four 6-demicubic lattices: It is also the 6-dimensional body centered cubic, the union of two 6-cube honeycombs in dual positions.
- + + + = + .
The kissing number of the D6* lattice is 12 (2n for n≥5). and its Voronoi tessellation is a trirectified 6-cubic honeycomb, containing all birectified 6-orthoplex Voronoi cell, .
Read more about this topic: 6-demicubic Honeycomb