D8 Lattice
The vertex arrangement of the 8-demicubic honeycomb is the D8 lattice. The 112 vertices of the rectified 8-orthoplex vertex figure of the 8-demicubic honeycomb reflect the kissing number 112 of this lattice. The best known is 240, from the E8 lattice and the 521 honeycomb.
The D8+ lattice (also called D82) can be constructed by the union of two D8 lattices. This packing is only a lattice for even dimensions. The kissing number is 240. (2n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8). It is identical to the E8 lattice]. ( contains as a subgroup of index 270.) At 8-dimensions, the 240 contacts contain both the 27=128 from lower dimension contact progression (2n-1), and 16*7=112 from higher dimensions (2n(n-1)).
- + = .
The D8* lattice (also called D84 and C82) can be constructed by the union of all four D8 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 D8* lattice is 16 (2n for n≥5). and its Voronoi tessellation is a quadrirectified 8-cubic honeycomb, containing all trirectified 8-orthoplex Voronoi cell, .
Read more about this topic: 8-demicubic Honeycomb