152 honeycomb
(No image)
Type	Uniform tessellation
Family	1k2 polytope
Schläfli symbol	{3,35,2}
Coxeter symbol	152
Coxeter-Dynkin diagram
8-face types	142 151
7-face types	132 141
6-face types	122 {31,3,1} {35}
5-face types	121 {34}
4-face type	111 {33}
Cells	{32}
Faces	{3}
Vertex figure	birectified 8-simplex: t2{37}
Coxeter group	${\displaystyle {\tilde {E))_{8))$, [35,2,1]

In geometry, the 1₅₂ honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 1₄₂ and 1₅₁ facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1_k2 polytope family.

Construction

It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space.

The facet information can be extracted from its Coxeter-Dynkin diagram.

Removing the node on the end of the 2-length branch leaves the 8-demicube, 1₅₁.

Removing the node on the end of the 5-length branch leaves the 1₄₂.

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 0₅₂.

Related polytopes and honeycombs

1k2 figures in n dimensions
Space	Finite						Euclidean	Hyperbolic
n	3	4	5	6	7	8	9	10
Coxeter group	E3=A2A1	E4=A4	E5=D5	E6	E7	E8	E9 = ${\displaystyle {\tilde {E))_{8))$ = E8+	E10 = ${\displaystyle {\bar {T))_{8))$ = E8++
Coxeter diagram
Symmetry (order)	[3−1,2,1]	[30,2,1]	[31,2,1]	[[32,2,1]]	[33,2,1]	[34,2,1]	[35,2,1]	[36,2,1]
Order	12	120	1,920	103,680	2,903,040	696,729,600	∞
Graph							-	-
Name	1−1,2	102	112	122	132	142	152	162