# 12-cube

(Redirected from Dodekeract)
12-cube
Rank12
TypeRegular
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3}
Elements
Henda24 hendekeracts
Daka264 dekeracts
Xenna1760 enneracts
Yotta7920 octeracts
Zetta25344 hepteracts
Exa59136 hexeracts
Peta101376 penteracts
Tera126720 tesseracts
Cells112640 cubes
Faces67584 squares
Edges24576
Vertices4096
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {3}}\approx 1.73205}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of external pieces24
Level of complexity1
Related polytopes
Army*
Regiment*
Dual12-orthoplex
ConjugateNone
Abstract & topological properties
Flag count1961990553600
Euler characteristic0
OrientableYes
Properties
SymmetryB12, order 1961990553600
Flag orbits1
ConvexYes
NatureTame

The 12-cube, also called the dodekeract or icositetrahendon, is a regular 12-polytope. It has 24 11-cubes as facets, joining 3 to a peak and 12 to a vertex.

It is the 12-dimensional hypercube. As such, it is a hexeract duoprism, tesseract trioprism, cube tetraprism and square hexaprism.

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

## Vertex coordinates

The vertices of a 12-cube of edge length 1, centered at the origin, are given by:

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