# Dekeract

(Redirected from 10-cube)
Dekeract
Rank10
TypeRegular
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${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90º
Height1
Central density1
Number of external pieces20
Level of complexity1
Related polytopes
ArmyDeker
RegimentDeker
DualChiliaicositetraxennon
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB10, order 3715891200
Flag orbits1
ConvexYes
Net count26941775019280[1]
NatureTame

The 10-cube, also called the icosaxennon, dekeract, or deker, is one of the 3 regular 10-polytopes. It has 20 8-cubes as facets, joining 3 to a 7-cube peak and 10 to a vertex.

It is the 10-dimensional hypercube. It is also a 5-cube duoprism and a square pentaprism.

It can be alternated into a 10-demicube, which is uniform.

## Vertex coordinates

The vertices of a 10-cube of edge length 1, centered at the origin, are given by:

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