The 6-demicubic honeycomb or demihexeractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 6-space. It is constructed as an alternation of the regular 6-cube honeycomb.
It is composed of two different types of facets. The 6-cubes become alternated into 6-demicubes h{4,3,3,3,3} and the alternated vertices create 6-orthoplex {3,3,3,3,4} facets.
The vertex arrangement of the 6-demicubic honeycomb is the D<sub>6</sub> 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 E<sub>6</sub> lattice and the 2<sub>22</sub> honeycomb.
The D lattice (also called D) can be constructed by the union of two D<sub>6</sub> lattices. This packing is only a lattice for even dimensions. The kissing number is 2<sup>5</sup>=32 (2<sup>n-1</sup> for n<8, 240 for n=8, and 2n(n-1) for n>8).
The D lattice (also called D and C) 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 D<sub>6</sub><sup>*</sup> lattice is 12 (2n for nâÂÂ¥5). and its Voronoi tessellation is a trirectified 6-cubic honeycomb, , containing all birectified 6-orthoplex Voronoi cell, .
There are three uniform construction symmetries of this tessellation. Each symmetry can be represented by arrangements of different colors on the 64 6-demicube facets around each vertex.