Hendekeract

Hendekeract
(OFF file)
Rank	11
Type	Regular
Space	Spherical
Notation
Coxeter diagram	x4o3o3o3o3o3o3o3o3o3o
Schläfli symbol	{4,3,3,3,3,3,3,3,3,3}
Elements
Daka	22 dekeracts
Xenna	220 enneracts
Yotta	1320 octeracts
Zetta	5280 hepteracts
Exa	14784 hexeracts
Peta	29568 penteracts
Tera	42240 tesseracts
Cells	42240 cubes
Faces	28160 squares
Edges	11264
Vertices	2048
Vertex figure	Hendecaxennon, edge length √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11}}{2} ≈ 1.65831$
Inradius	$\frac12 = 0.5$
Hypervolume	1
Dixennal angle	90°
Height	1
Central density	1
Number of pieces	22
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Dischiliatetracontoctadakon
Conjugate	None
Abstract properties
Euler characteristic	2
Topological properties
Orientable	Yes
Properties
Symmetry	B11, order 81749606400
Convex	Yes
Nature	Tame

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.

Vertex coordinates

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

• $\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right).$