5-simplex honeycomb

In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively in the whole honeycomb.

5-simplex honeycomb
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Type	Uniform 5-honeycomb
Family	Simplectic honeycomb
Schläfli symbol	{3[6]}
Coxeter diagram
5-face types	{34} , t1{34} t2{34}
4-face types	{33} , t1{33}
Cell types	{3,3} , t1{3,3}
Face types	{3}
Vertex figure	t0,4{34}
Coxeter groups	${\displaystyle {\tilde {A}}_{5}}$×2, <[3[6]]>
Properties	vertex-transitive