# Great enneagram

Great enneagram
Rank2
TypeRegular
Notation
Bowers style acronymGeng
Coxeter diagramx9/4o ()
Schläfli symbol{9/4}
Elements
Edges9
Vertices9
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {4\pi }{9}}}}\approx 0.50771}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {4\pi }{9}}}}\approx 0.088163}$
Area${\displaystyle {\frac {9}{4\tan {\frac {4\pi }{9}}}}\approx 0.39674}$
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
Flag orbits1
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)).