# Great enneagram

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

The great enneagram, or geng, 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)).