(Redirected from 11-orthoplex)
Rank11
TypeRegular
SpaceSpherical
Notation
Coxeter diagramo4o3o3o3o3o3o3o3o3o3x
Schläfli symbol{3,3,3,3,3,3,3,3,3,4}
Elements
Daka2048 hendecaxenna
Xenna11624 decayotta
Yotta28160 enneazetta
Zetta42240 octaexa
Exa42240 heptapeta
Peta29568 hexatera
Tera14784 pentachora
Cells5280 tetrahedra
Faces1320 triangles
Edges220
Vertices22
Vertex figureChiliaicositetraxennon, edge length 1
Measures (edge length 1)
Circumradius$\frac{\sqrt2}{2} \approx 0.70711$ Inradius$\frac{\sqrt{22}}{22} \approx 0.21320$ Hypervolume$\frac{\sqrt2}{1247400} \approx 0.0000011337$ Dihedral angle$\arccos\left(-\frac{9}{11}\right) \approx 144.90320°$ Height$\frac{\sqrt{22}}{11} \approx 0.42640$ Central density1
Number of pieces2048
Level of complexity1
Related polytopes
Army*
Regiment*
DualHendekeract
ConjugateNone
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryB11, order 81749606400
ConvexYes
NatureTame

The dischiliatetracontoctadakon, also called the hendecacross or 11-orthoplex, is one of the 3 regular polydaka. It has 2048 regular hendecaxenna as facets, joining 4 to a yotton and 1024 to a vertex in a chiliaicositetraxennal arrangement. It is the 11-dimensional orthoplex.

## Vertex coordinates

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

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