11-orthoplex

11-orthoplex
Rank11
TypeRegular
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${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Inradius${\displaystyle {\frac {\sqrt {22}}{22}}\approx 0.21320}$
Hypervolume${\displaystyle {\frac {\sqrt {2}}{1247400}}\approx 0.0000011337}$
Dihedral angle${\displaystyle \arccos \left(-{\frac {9}{11}}\right)\approx 144.90320^{\circ }}$
Height${\displaystyle {\frac {\sqrt {22}}{11}}\approx 0.42640}$
Central density1
Number of external pieces2048
Level of complexity1
Related polytopes
Army*
Regiment*
DualHendekeract
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB11, order 81749606400
ConvexYes
NatureTame

The 11-orthoplex, also called the hendecacross or 11-orthoplex, is a regular polydakon. It has 2048 regular hendecaxenna as facets, joining 4 to a peak 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:

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