5-demicubic honeycomb

The 5-demicube honeycomb (or demipenteractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space. It is constructed as an alternation of the regular 5-cube honeycomb.

Demipenteractic honeycomb
(No image)
Type	Uniform 5-honeycomb
Family	Alternated hypercubic honeycomb
Schläfli symbols	h{4,3,3,3,4} h{4,3,3,31,1} ht0,5{4,3,3,3,4} h{4,3,3,4}h{∞} h{4,3,31,1}h{∞} ht0,4{4,3,3,4}h{∞} h{4,3,4}h{∞}h{∞} h{4,31,1}h{∞}h{∞}
Coxeter diagrams	= =
Facets	{3,3,3,4} h{4,3,3,3}
Vertex figure	t1{3,3,3,4}
Coxeter group	${\displaystyle {\tilde {B}}_{5}}$ [4,3,3,31,1] ${\displaystyle {\tilde {D}}_{5}}$ [31,1,3,31,1]

It is the first tessellation in the demihypercube honeycomb family which, with all the next ones, is not regular, being composed of two different types of uniform facets. The 5-cubes become alternated into 5-demicubes h{4,3,3,3} and the alternated vertices create 5-orthoplex {3,3,3,4} facets.