Tridekeract

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Tridekeract
13-cube.png
Rank13
TypeRegular
SpaceSpherical
Info
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3}
SymmetryB13, order 51011754393600
Army*
Regiment*
Elements
Vertex figureTridecahendon, edge length 2
Doka26 dodekeracts
Henda312 hendekeracts
Daka2288 dekeracts
Xenna11440 enneracts
Yotta41184 octeracts
Zetta109824 hepteracts
Exa219648 hexeracts
Peta329472 penteracts
Tera366080 tesseracts
Cells292864 cubes
Faces159744 squares
Edges53248
Vertices8192
Measures (edge length 1)
Circumradius13/2 ≈ 1.80278
Inradius1/2 = 0.5
Hypervolume1
Dixennal angle90°
Central density1
Euler characteristic2
Related polytopes
DualOctachiliahecatonenneacontadidokon
ConjugateTridekeract
Properties
ConvexYes
OrientableYes
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[edit | edit source]

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

  • (±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2).