# 9-cube

9-cube
Rank9
TypeRegular
Notation
Bowers style acronymEnne
Coxeter diagramx4o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3}
Tapertopic notation111111111
Toratopic notationIIIIIIIII
Bracket notation[IIIIIIIII]
Elements
Yotta18 octeracts
Zetta144 hepteracts
Exa672 hexeracts
Peta2016 penteracts
Tera4032 tesseracts
Cells5376 cubes
Faces4608 squares
Edges2304
Vertices512
Vertex figureEnneazetton, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {3}{2}}=1.5}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Diyottal angle90°
Height1
Central density1
Number of external pieces18
Level of complexity1
Related polytopes
ArmyEnne
RegimentEnne
DualPentacosidodecayotton
ConjugateNone
Abstract & topological properties
Flag count185794560
Euler characteristic2
OrientableYes
Properties
SymmetryB9, order 185794560
Flag orbits1
ConvexYes
Net count248639631948[1]
NatureTame

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:

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