11-orthoplex

11-orthoplex
Rank	11
Type	Regular
Notation
Coxeter diagram	o4o3o3o3o3o3o3o3o3o3x ()
Schläfli symbol	{3,3,3,3,3,3,3,3,3,4}
Elements
Daka	2048 hendecaxenna
Xenna	11624 decayotta
Yotta	28160 enneazetta
Zetta	42240 octaexa
Exa	42240 heptapeta
Peta	29568 hexatera
Tera	14784 pentachora
Cells	5280 tetrahedra
Faces	1320 triangles
Edges	220
Vertices	22
Vertex figure	Chiliaicositetraxennon, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Inradius	${\frac {\sqrt {22}}{22}}\approx 0.21320$
Hypervolume	${\frac {\sqrt {2}}{1247400}}\approx 0.0000011337$
Dihedral angle	$\arccos \left(-{\frac {9}{11}}\right)\approx 144.90320^{\circ }$
Height	${\frac {\sqrt {22}}{11}}\approx 0.42640$
Central density	1
Number of external pieces	2048
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Hendekeract
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B11, order 81749606400
Convex	Yes
Nature	Tame

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:

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