14-cube

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14-cube
Rank14
TypeRegular
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Tradaka28 tridekeracts
Doka364 dodekeracts
Henda2912 hendekeracts
Daka16016 dekeracts
Xenna64064 enneracts
Yotta192192 octeracts
Zetta439296 hepteracts
Exa768768 hexeracts
Peta1025024 penteracts
Tera1025024 tesseracts
Cells745472 cubes
Faces372736 squares
Edges114688
Vertices16384
Vertex figureTetradecadokon, edge length 2
Measures (edge length 1)
Circumradius
Inradius
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[edit | edit source]

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

  • .