# 9-orthoplex

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${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Inradius${\displaystyle {\frac {\sqrt {2}}{6}}\approx 0.23570}$
Hypervolume${\displaystyle {\frac {\sqrt {2}}{22680}}\approx 0.000062355}$
Diyottal angle${\displaystyle \arccos \left(-{\frac {7}{9}}\right)\approx 141.05756^{\circ }}$
Height${\displaystyle {\frac {\sqrt {2}}{3}}\approx 0.47140}$
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

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

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