 Rank14
TypeRegular
SpaceSpherical
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Doka364 dodekeracts
Henda2912 hendekeracts
Daka16016 dekeracts
Xenna64064 enneracts
Yotta192192 octeracts
Zetta439296 hepteracts
Exa768768 hexeracts
Peta1025024 penteracts
Tera1025024 tesseracts
Cells745472 cubes
Faces372736 squares
Edges114688
Vertices16384
Measures (edge length 1)
Circumradius$\frac{\sqrt{14}}{2} \approx 1.87083$ Inradius$\frac12 = 0.5$ Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of pieces28
Level of complexity1
Related polytopes
Army*
Regiment*
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB14, order 1428329123020800
ConvexYes
NatureTame

The tetradekeract, also called the 14-cube or icosioctatradakon, is one of the 3 regular polytradaka. It has 28 tridekeracts as facets, joining 3 to a hendon and 14 to a vertex.

It is the 14-dimensional hypercube. As such it is a hepteract duoprism and square heptaprism.

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

## Vertex coordinates

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

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