11-cube

11-cube
Rank11
TypeRegular
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3,3}
Elements
Daka22 10-cubes
Xenna220 9-cubes
Yotta1320 8-cubes
Zetta5280 7-cubes
Exa14784 6-cubes
Peta29568 5-cubes
Tera42240 tesseracts
Cells42240 cubes
Faces28160 squares
Edges11264
Vertices2048
Vertex figure10-simplex, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {11}}{2}}\approx 1.65831}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of external pieces22
Level of complexity1
Related polytopes
Army*
Regiment*
Dual11-orthoplex
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB11, order 81749606400
Flag orbits1
ConvexYes
NatureTame

The 11-cube, also called the hendekeract or icosididakon, is one of the 3 regular 11-polytopes. It has 22 10-cubes as facets, joining 3 to a yotton peak and 11 to a vertex.

It is the 11-dimensional hypercube.

It can be alternated into a 11-demicube, which is uniform.

A regular 11-simplex of edge length 6 can be inscribed in the 11-cube. The next largest simplex that can be inscribed in a hypercube is the 15-simplex.[1]

Vertex coordinates

The vertices of a 11-cube of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$.

References

1. Sloane, N. J. A. (ed.). "Sequence A019442". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.