Quarter hypercubic honeycomb

In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4} or Coxeter symbol q&delta;4 representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group $${\tilde{D}}_{n-1}$$ for n ≥ 5, with $${\tilde{D}}_4$$ = $${\tilde{A}}_4$$ and for quarter n-cubic honeycombs $${\tilde{D}}_5$$ = $${\tilde{B}}_5$$.