D7 Lattice
The vertex arrangement of the 7-demicubic honeycomb is the D7 lattice. The 84 vertices of the rectified 7-orthoplex vertex figure of the 7-demicubic honeycomb reflect the kissing number 84 of this lattice. The best known is 126, from the E7 lattice and the 331 honeycomb.
The D7+ packing (also called D72) can be constructed by the union of two D7 lattices. The Dn+ packings form lattices only in even dimensions. The kissing number is 26=64 (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8).
- +
The D7* lattice (also called D74 and C72) can be constructed by the union of all four 7-demicubic lattices: It is also the 7-dimensional body centered cubic, the union of two 7-cube honeycombs in dual positions.
- + + + = + .
The kissing number of the D7* lattice is 14 (2n for n≥5) and its Voronoi tessellation is a quadritruncated 7-cubic honeycomb, containing all with tritruncated 7-orthoplex, Voronoi cells.
Read more about this topic: 7-demicubic Honeycomb