Alternated hypercubic honeycomb

In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation. It is given a Schläfli symbol h{4,3...3,4} representing the regular form with half the vertices removed and containing the symmetry of Coxeter group $${\tilde{B}}_{n-1}$$ for n ≥ 4. A lower symmetry form $${\tilde{D}}_{n-1}$$ can be created by removing another mirror on an order-4 peak.

The alternated hypercube facets become demihypercubes, and the deleted vertices create new orthoplex facets. The vertex figure for honeycombs of this family are rectified orthoplexes.

These are also named as h&delta;n for an (n-1)-dimensional honeycomb.