# 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$\frac{\sqrt{10}}{2} \approx 1.58114$ Inradius$\frac12 = 0.5$ Hypervolume1
Dixennal angle90º
Height1
Central density1
Number of pieces20
Level of complexity1
Related polytopes
ArmyDeker
RegimentDeker
DualChiliaicositetraxennon
ConjugateNone
Abstract properties
Net count26941775019280
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:

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