9-cube

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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
Inradius
Hypervolume1
Diyottal angle90º
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
ConvexYes
Net count248639631948[1]
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[edit | edit source]

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

  • .

External links[edit | edit source]

References[edit | edit source]

  1. "A091159". The On-line Encyclopedia of Integer Sequences. Retrieved 2022-12-07.