# Tridekeract

Tridekeract
Rank13
TypeRegular
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3}
Elements
Doka26 dodekeracts
Henda312 hendekeracts
Daka2288 dekeracts
Xenna11440 enneracts
Yotta41184 octeracts
Zetta109824 hepteracts
Exa219648 hexeracts
Peta329472 penteracts
Tera366080 tesseracts
Cells292864 cubes
Faces159744 squares
Edges53248
Vertices8192
Vertex figureTridecahendon, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {13}}{2}}\approx 1.80278}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90°
Central density1
Number of external pieces26
Level of complexity1
Related polytopes
Army*
Regiment*
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB13, order 51011754393600
ConvexYes
NatureTame

The tridekeract, also called the 13-cube or icosihexadokon, is one of the 3 regular polydoka. It has 26 dodekeracts as facets, joining 3 to a dakon and 13 to a vertex.

It is the 13-dimensional hypercube.

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

## Vertex coordinates

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

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