# Enneract

Enneract Rank9
TypeRegular
SpaceSpherical
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$\frac32 = 1.5$ Inradius$\frac12 = 0.5$ Hypervolume1
Diyottal angle90º
Height1
Central density1
Number of pieces18
Level of complexity1
Related polytopes
ArmyEnne
RegimentEnne
DualPentacosidodecayotton
ConjugateNone
Abstract properties
Net count248639631948
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryB9, order 185794560
ConvexYes
NatureTame

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

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

It can be alternated into a demienneract, which is uniform.

## Vertex coordinates

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

• $\left(\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12\right).$ 