5-demicubic 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]

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.

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.