# Dekeract

Dekeract
Rank10
TypeRegular
SpaceSpherical
Notation
Bowers style acronymDeker
Coxeter diagramx4o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3}
Tapertopic notation1111111111
Toratopic notationIIIIIIIIII
Bracket notation[IIIIIIIIII]
Elements
Xenna20 enneracts
Yotta180 octeracts
Zetta960 hepteracts
Exa3360 hexeracts
Peta8064 penteracts
Tera13440 tesseracts
Cells15360 cubes
Faces11520 squares
Edges5120
Vertices1024
Vertex figureDecayotton, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{10}}{2} \approx 1.58114}$
Inradius${\displaystyle \frac12 = 0.5}$
Hypervolume1
Dixennal angle90º
Height1
Central density1
Number of pieces20
Level of complexity1
Related polytopes
ArmyDeker
RegimentDeker
DualChiliaicositetraxennon
ConjugateNone
Abstract properties
Net count26941775019280[1]
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB10, order 3715891200
ConvexYes
NatureTame

The dekeract, or deker, also called the 10-cube, or icosaxennon, is one of the 3 regular polyxenna. It has 20 enneracts as facets, joining 3 to a hepteract peak and 10 to a vertex.

It is the 10-dimensional hypercube. It is also a penteract duoprism and a square pentaprism.

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

## Vertex coordinates

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

• ${\displaystyle \left(\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12\right).}$