# Great enneagram

Great enneagram
Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGeng
Coxeter diagramx9/4o ()
Schläfli symbol{9/4}
Elements
Edges9
Vertices9
Measures (edge length 1)
Circumradius${\displaystyle \frac{1}{2\sin\frac{4\pi}{9}} ≈ 0.50771}$
Inradius${\displaystyle \frac{1}{2\tan\frac{4\pi}{9}} ≈ 0.088163}$
Area${\displaystyle \frac{9}{4\tan\frac{4\pi}{9}} ≈ 0.39674}$
Angle20°
Central density4
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length ${\displaystyle 2\cos\frac{4\pi}{9}}$
DualGreat enneagram
ConjugatesEnneagon, enneagram
Convex coreEnneagon
Abstract & topological properties
Flag count18
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9), order 18
ConvexNo
NatureTame

The great enneagram is a non-convex polygon with 9 sides. Its created by taking the third stellation of an enneagon. A regular great enneagram has equal sides and equal angles.

It is one of two regular 9-sided star polygons, the other being the enneagram.

## Vertex coordinates

Coordinates for a regular great enneagram of edge length 2sin(4π/9), centered at the origin, are:

• (1, 0),
• (cos(2π/9), ±sin(2π/9)),
• (cos(4π/9), ±sin(4π/9)),
• (–1/2, ±3/2),
• (cos(8π/9), ±sin(8π/9)).