# 14-cube

14-cube
Rank14
TypeRegular
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${\displaystyle {\frac {\sqrt {14}}{2}}\approx 1.87083}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of external pieces28
Level of complexity1
Related polytopes
Army*
Regiment*
Dual14-orthoplex
ConjugateNone
Abstract & topological properties
Flag count1428329123020800
Euler characteristic0
OrientableYes
Properties
SymmetryB14, order 1428329123020800
Flag orbits1
ConvexYes
NatureTame

The 14-cube, also called the tetradekeract or icosioctatradakon, is one of the 3 regular 14-polytopes. It has 28 13-cubes as facets, joining 3 to a hendon peak and 14 to a vertex.

It is the 14-dimensional hypercube. As such it is a 7-cube duoprism and square heptaprism.

It can be alternated into a 14-demicube, which is uniform.

## Vertex coordinates

The vertices of a 14-cube of edge length 1, centered at the origin, are given by:

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