# Tridekeract

Tridekeract Rank13
TypeRegular
SpaceSpherical
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$\frac{\sqrt{13}}{2} ≈ 1.80278$ Inradius$\frac12 = 0.5$ Hypervolume1
Dixennal angle90°
Central density1
Number of pieces26
Level of complexity1
Related polytopes
Army*
Regiment*
ConjugateNone
Abstract properties
Euler characteristic2
Topological properties
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:

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