Chiliaicositetraxennon

Chiliaicositetraxennon
(OFF file)
Rank	10
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Ka
Coxeter diagram	o4o3o3o3o3o3o3o3o3x ()
Schläfli symbol	{3,3,3,3,3,3,3,3,4}
Elements
Xenna	1024 decayotta
Yotta	5120 enneazetta
Zetta	11520 octaexa
Exa	15360 heptapeta
Peta	13440 hexatera
Tera	8064 pentachora
Cells	3360 tetrahedra
Faces	960 triangles
Edges	180
Vertices	20
Vertex figure	Pentacosidodecayotton, edge length 1
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} \approx 0.70711$
Inradius	$\frac{\sqrt5}{10} \approx 0.22361$
Hypervolume	$\frac{1}{113400} \approx 0.0000088183$
Dixennal angle	$\arccos\left(-\frac45\right) \approx 143.13010^\circ$
Height	$\frac{\sqrt5}{5} \approx 0.44721$
Central density	1
Number of pieces	1024
Level of complexity	1
Related polytopes
Army	Ka
Regiment	Ka
Dual	Dekeract
Conjugate	None
Abstract properties
Net count	26941775019280
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B10, order 3715891200
Convex	Yes
Nature	Tame

The chiliaicositetraxennon, or ka, also called the decacross or 10-orthoplex, is one of the 3 regular polyxenna. It has 1024 regular decayotta as facets, joining 4 to an octaexon peak and 512 to a vertex in a pentacosidodecayottal arrangement. It is the 10-dimensional orthoplex. It is also a triacontaditeron duotegum and square pentategum.

Vertex coordinates

The vertices of a regular chiliaicositetraxennon of edge length 1, centered at the origin, are given by all permutations of:

• $\left(\pm\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).$

External links

• Klitzing, Richard. "ka".

• Wikipedia Contributors. "10-orthoplex".