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Source: 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 qδ4 representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group

D
~

n
−
1

{\displaystyle {\tilde {D}}_{n-1}}

for n ≥ 5, with

D
~

4

{\displaystyle {\tilde {D}}_{4}}

=

A
~

4

{\displaystyle {\tilde {A}}_{4}}

and for quarter n-cubic honeycombs

D
~

5

{\displaystyle {\tilde {D}}_{5}}

=

B
~

5

{\displaystyle {\tilde {B}}_{5}}

.