(Redirected from 13-orthoplex)
Rank13
TypeRegular
SpaceSpherical
Notation
Coxeter diagramo4o3o3o3o3o3o3o3o3o3o3o3x
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Doka8192 tridecahenda
Daka159744 hendecaxenna
Xenna292864 decayotta
Yotta366080 enneazetta
Zetta329472 octaexa
Exa219648 heptapeta
Peta109824 hexatera
Tera41184 pentachora
Cells11440 tetrahedra
Faces2288 triangles
Edges312
Vertices26
Vertex figureTetrachiliaenneacontahexahendon, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2}{2} \approx 0.70711}$
Inradius${\displaystyle \frac{\sqrt{26}}{26} \approx 0.19612}$
Hypervolume${\displaystyle \frac{\sqrt2}{97297200} \approx 1.4535×10^{-8}}$
Dihedral angle${\displaystyle \arccos\left(-\frac{11}{13}\right) \approx 147.79577°}$
Height${\displaystyle \frac{\sqrt{26}}{13} \approx 0.39223}$
Central density1
Number of pieces8192
Level of complexity1
Related polytopes
Army*
Regiment*
DualTridekeract
ConjugateNone
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryB13, order 51011754393600
ConvexYes
NatureTame

The octachiliahecatonenneacontadidokon, also called the tridecacross or 13-orthoplex, is one of the 3 regular polydoka. It has 8192 regular tridecahenda as facets, joining 4 to a dakon and 4096 to a vertex in a tetrachiliaenneacontahexahendal arrangement. It is the 13-dimensional orthoplex.

## Vertex coordinates

The vertices of a regular octachiliahecatonenneacontadidokon of edge length 1, centered at the origin, are given by all permutations of:

• ${\displaystyle \left(\pm\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).}$