Great enneagram

Great enneagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Geng
Coxeter diagram	x9/4o ()
Schläfli symbol	{9/4}
Elements
Edges	9
Vertices	9
Vertex figure	Dyad, length 2cos(4π/9)
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	$\frac{9}{4\tan\frac{4\pi}{9}} ≈ 0.39674$
Angle	20°
Central density	4
Number of external pieces	18
Level of complexity	2
Related polytopes
Army	En, edge length $2\cos\frac{4\pi}{9}$
Dual	Great enneagram
Conjugates	Enneagon, enneagram
Convex core	Enneagon
Abstract & topological properties
Flag count	18
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9), order 18
Convex	No
Nature	Tame

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)).

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

• Wikipedia Contributors. "Enneagram (geometry)".