The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 8-space. It is constructed as an alternation of the regular 8-cubic honeycomb.
It is composed of two different types of facets. The 8-cubes become alternated into 8-demicubes h{4,3,3,3,3,3,3} and the alternated vertices create 8-orthoplex {3,3,3,3,3,3,4} facets .
The vertex arrangement of the 8-demicubic honeycomb is the D<sub>8</sub> 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 E<sub>8</sub> lattice and the 5<sub>21</sub> honeycomb.
contains as a subgroup of index 270. Both and can be seen as affine extensions of from different nodes:
The D lattice (also called D) can be constructed by the union of two D8 lattices. This packing is only a lattice for even dimensions. The kissing number is 240. (2<sup>n-1</sup> for n<8, 240 for n=8, and 2n(n-1) for n>8). It is identical to the E8 lattice. At 8-dimensions, the 240 contacts contain both the 2<sup>7</sup>=128 from lower dimension contact progression (2<sup>n-1</sup>), and 16*7=112 from higher dimensions (2n(n-1)).
The D lattice (also called D and C) 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 D lattice is 16 (2n for nâÂÂ¥5). and its Voronoi tessellation is a quadrirectified 8-cubic honeycomb, , containing all trirectified 8-orthoplex Voronoi cell, .
There are three uniform construction symmetries of this tessellation. Each symmetry can be represented by arrangements of different colors on the 256 8-demicube facets around each vertex.