10-orthoplex

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10-orthoplex
Rank10
TypeRegular
Notation
Bowers style acronymKa
Coxeter diagramx3o3o3o3o3o3o3o3o4o ()
Schläfli symbol{3,3,3,3,3,3,3,3,4}
Elements
Xenna1024 decayotta
Yotta5120 enneazetta
Zetta11520 octaexa
Exa15360 heptapeta
Peta13440 hexatera
Tera8064 pentachora
Cells3360 tetrahedra
Faces960 triangles
Edges180
Vertices20
Vertex figurePentacosidodecayotton, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dixennal angle
Height
Central density1
Number of external pieces1024
Level of complexity1
Related polytopes
ArmyKa
RegimentKa
DualDekeract
ConjugateNone
Abstract & topological properties
Flag count3715891200
Euler characteristic0
OrientableYes
Properties
SymmetryB10, order 3715891200
ConvexYes
Net count26941775019280
NatureTame

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

Vertex coordinates[edit | edit source]

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

  • .

External links[edit | edit source]