# Enneagram

Enneagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymEng
Coxeter diagramx9/2o (     )
Schläfli symbol{9/2}
Elements
Edges9
Vertices9
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\frac{2\pi}{9}} ≈ 0.77786$ Inradius$\frac{1}{2\tan\frac{2\pi}{9}} ≈ 0.59588$ Area$\frac{9}{4\tan\frac{2\pi}{9}} ≈ 2.68145$ Angle100°
Central density2
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length $\frac{1}{2\cos\frac\pi9}$ DualEnneagram
ConjugatesEnneagon, great enneagram
Convex coreEnneagon
Abstract & topological properties
Flag count18
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9), order 18
ConvexNo
NatureTame

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

It is one of two regular 9-sided star polygons, the other being the great enneagram. The name "enneagram" is often used to describe either of these two shapes.

## Vertex coordinates

Coordinates for a regular enneagram of edge length 2sin(2π/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)).