[1] The 84 vertices of the rectified 7-orthoplex vertex figure of the 7-demicubic honeycomb reflect the kissing number 84 of this lattice.
The D+7 packing (also called D27) can be constructed by the union of two D7 lattices.
[3] The D*7 lattice (also called D47 and C27) can be constructed by the union of all four 7-demicubic lattices:[4] It is also the 7-dimensional body centered cubic, the union of two 7-cube honeycombs in dual positions.
The kissing number of the D*7 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.
Each symmetry can be represented by arrangements of different colors on the 128 7-demicube facets around each vertex.