# Enneagram

Enneagram
Rank2
TypeRegular
Notation
Bowers style acronymEng
Coxeter diagramx9/2o ()
Schläfli symbol{9/2}
Elements
Edges9
Vertices9
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {2\pi }{9}}}}\approx 0.77786}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {2\pi }{9}}}}\approx 0.59588}$
Area${\displaystyle {\frac {9}{4\tan {\frac {2\pi }{9}}}}\approx 2.68145}$
Angle100°
Central density2
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length ${\displaystyle {\frac {1}{2\cos {\frac {\pi }{9}}}}}$
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 ${\displaystyle 2\sin(2\pi /9)}$, centered at the origin, are:

• ${\displaystyle (1,0)}$,
• ${\displaystyle (\cos(2\pi /9),\pm \sin(2\pi /9))}$,
• ${\displaystyle (\cos(4\pi /9),\pm \sin(4\pi /9))}$,
• ${\displaystyle (-1/2,\pm {\sqrt {3}}/2)}$,
• ${\displaystyle (\cos(8\pi /9),\pm \sin(8\pi /9))}$.