8-demicubic honeycomb


The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation 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 and the alternated vertices create 8-orthoplex facets.

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.
contains as a subgroup of index 270. Both and can be seen as affine extensions of from different nodes:
The D lattice can be constructed by the union of two D8 lattices. This packing is only a lattice for even dimensions. The kissing number is 240.. It is identical to the E8 lattice. At 8-dimensions, the 240 contacts contain both the 27=128 from lower dimension contact progression, and 16*7=112 from higher dimensions.
The D lattice 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. and its Voronoi tessellation is a quadrirectified 8-cubic honeycomb,, containing all trirectified 8-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 256 8-demicube facets around each vertex.
Coxeter groupSchläfli symbolCoxeter-Dynkin diagramVertex figure
Symmetry		Facets/verf
=
= 		h =
256: 8-demicube
16: 8-orthoplex
=
= 		h =
128+128: 8-demicube
16: 8-orthoplex
2×½ = ht0,8128+64+64: 8-demicube
16: 8-orthoplex