Hendekeract

Hendekeract
Rank11
TypeRegular
SpaceSpherical
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3}
Elements
Daka22 dekeracts
Xenna220 enneracts
Yotta1320 octeracts
Zetta5280 hepteracts
Exa14784 hexeracts
Peta29568 penteracts
Tera42240 tesseracts
Cells42240 cubes
Faces28160 squares
Edges11264
Vertices2048
Vertex figureHendecaxennon, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{11}}{2} ≈ 1.65831}$
Inradius${\displaystyle \frac12 = 0.5}$
Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of pieces22
Level of complexity1
Related polytopes
Army*
Regiment*
ConjugateNone
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryB11, order 81749606400
ConvexYes
NatureTame

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

It is the 11-dimensional hypercube.

It can be alternated into a demihendekeract, which is uniform.

A regular dodecadakon of edge length 6 can be inscribed in the hendekeract. The next largest simplex that can be inscribed in a hypercube is the hexadecatedakon.[1]

Vertex coordinates

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

• ${\displaystyle \left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right).}$

References

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