Dodekeract

From Polytope Wiki
(Redirected from 12-hypercube)
Jump to navigation Jump to search
Dodekeract
12-cube.svg
Rank12
TypeRegular
SpaceSpherical
Info
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3}
SymmetryB12, order 1961990553600
Army*
Regiment*
Elements
Vertex figureDodecadakon, edge length 2
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)
Circumradius3 ≈ 1.73205
Inradius1/2 = 0.5
Hypervolume1
Dixennal angle90°
Central density1
Euler characteristic0
Related polytopes
DualTetrachiliaenneacontahexahendon
ConjugateDodekeract
Properties
ConvexYes
OrientableYes
NatureTame

The dodekeract, also called the 12-cube or icositetrahendon, is one of the 3 regular polyhenda. It has 24 hendekeracts as facets, joining 3 to a xennon 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[edit | edit source]

The vertices of a dodekeract 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, ±1/2, ±1/2).