9-cube

9-cube
(OFF file)
Rank	9
Type	Regular
Notation
Bowers style acronym	Enne
Coxeter diagram	x4o3o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3,3}
Tapertopic notation	111111111
Toratopic notation	IIIIIIIII
Bracket notation	[IIIIIIIII]
Elements
Yotta	18 octeracts
Zetta	144 hepteracts
Exa	672 hexeracts
Peta	2016 penteracts
Tera	4032 tesseracts
Cells	5376 cubes
Faces	4608 squares
Edges	2304
Vertices	512
Vertex figure	Enneazetton, edge length √2
Measures (edge length 1)
Circumradius	${\frac {3}{2}}=1.5$
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	1
Diyottal angle	90°
Height	1
Central density	1
Number of external pieces	18
Level of complexity	1
Related polytopes
Army	Enne
Regiment	Enne
Dual	Pentacosidodecayotton
Conjugate	None
Abstract & topological properties
Flag count	185794560
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B9, order 185794560
Flag orbits	1
Convex	Yes
Net count	248639631948
Nature	Tame

The enneract, or enne, also called the 9-cube or octadecayotton, is one of the 3 regular 9-polytopes. It has 18 8-cubes as facets, joining 3 to a 6-cube peak and 9 to a vertex.

It is the 9-dimensional hypercube. It is also a cube trioprism.

It can be alternated into a 9-demicube, which is uniform.

Vertex coordinates

The vertices of an enneract of edge length 1, centered at the origin, are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$.

External links

• Klitzing, Richard. "enne".
• Wikipedia contributors. "9-cube".