9-orthoplex

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9-orthoplex
Rank9
TypeRegular
Notation
Bowers style acronymVee
Coxeter diagramo4o3o3o3o3o3o3o3x ()
Schläfli symbol{3,3,3,3,3,3,3,4}
Bracket notation<IIIIIIIII>
Elements
Yotta512 enneazetta
Zetta2304 octaexa
Exa4608 heptapeta
Peta5376 hexatera
Tera4032 pentachora
Cells2016 tetrahedra
Faces672 triangles
Edges144
Vertices18
Vertex figure8-orthoplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Diyottal angle
Height
Central density1
Number of external pieces512
Level of complexity1
Related polytopes
ArmyVee
RegimentVee
Dual9-cube
ConjugateNone
Abstract & topological properties
Flag count185794560
Euler characteristic2
OrientableYes
Properties
SymmetryB9, order 185794560
Flag orbits1
ConvexYes
Net count248639631948
NatureTame

The 9-orthoplex, also called the enneacross, pentacosidodecayotton, or vee, is one of the 3 regular 9-polytopes. It has 512 regular 8-simplices as facets, joining 4 to a 6-simplex peak and 256 to a vertex in a 8-orthoplecial arrangement. It is the 9-dimensional orthoplex. It is also an octahedron triotegum.

Vertex coordinates[edit | edit source]

The vertices of a regular 9-orthoplex of edge length 1, centered at the origin, are given by all permutations of:

  • .

External links[edit | edit source]