6-demicubic honeycomb
The 6-demicubic honeycomb or demihexeractic honeycomb is a uniform space-filling tessellation 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 and the alternated vertices create 6-orthoplex facets.
D6 lattice
The vertex arrangement of the 6-demicubic honeycomb is the D6 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 E6 lattice and the 222 honeycomb.The D lattice can be constructed by the union of two D6 lattices. This packing is only a lattice for even dimensions. The kissing number is 25=32.
The D lattice 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 D6* lattice is 12. and its Voronoi tessellation is a trirectified 6-cubic honeycomb,, containing all birectified 6-orthoplex Voronoi cell,.
Symmetry constructions
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.| Coxeter group | Schläfli symbol | Coxeter-Dynkin diagram | Vertex figure Symmetry | Facets/verf |
| = = | h | = | 64: 6-demicube 12: 6-orthoplex | |
| = = | h | = | 32+32: 6-demicube 12: 6-orthoplex | |
| ½ = | ht0,6 | 32+16+16: 6-demicube 12: 6-orthoplex |