Dekeract

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Dekeract
10-cube.svg
Rank10
TypeRegular
SpaceSpherical
Bowers style acronymDeker
Info
Coxeter diagramx4o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3}
SymmetryBC10, order 3715891200
ArmyDeker
RegimentDeker
Elements
Vertex figureDecayotton, edge length 2
Xenna20 enneracts
Yotta180 octeracts
Zetta960 hepteracts
Exa3360 hexeracts
Peta8064 penteracts
Tera13440 tesseracts
Cells15360 cubes
Faces11520 squares
Edges5120
Vertices1024
Measures (edge length 1)
Circumradius10/2 ≈ 1.58114
Inradius1/2 = 0.5
Hypervolume1
Dixennal angle90º
Central density1
Euler characteristic0
Related polytopes
DualChiliaicositetraxennon
ConjugateDekeract
Properties
ConvexYes
OrientableYes
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[edit | edit source]

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

  • (±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2).

External links[edit | edit source]