Chiliaicositetraxennon

{{Infobox polytope 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.
 * type=Regular
 * dim = 10
 * image = 10-orthoplex.svg
 * off=Chiliaicositetraxennon.off
 * obsa = Ka
 * 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
 * verf = Pentacosidodecayotton, edge length 1
 * schlafli = {3,3,3,3,3,3,3,3,4}
 * coxeter = o4o3o3o3o3o3o3o3o3x ({{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}})
 * army=Ka
 * reg =Ka
 * symmetry = B{{sub|10}}, order 3715891200
 * circum = $$\frac{\sqrt2}{2} ≈ 0.70711$$
 * inrad = $$\frac{\sqrt5}{10} ≈ 0.22361$$
 * height = $$\frac{\sqrt5]{5} ≈ 0.44721$$
 * hypervolume = $$\frac{1}{113400} ≈ 0.0000088183$$
 * dix = $$\arccos\left(-\frac45\right) ≈ 143.13010º$$
 * pieces = 1024
 * loc = 1
 * dual=Dekeract
 * conjugate=None
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a regular chiliaicositetraxennon of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).$$