Fissal enneagram

Fissal enneagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Fen
Schläfli symbol	{9/3}
Elements
Components	3 triangles
Edges	9
Vertices	9
Vertex figure	Dyad, length 1
Measures (edge length 1)
Circumradius	$\frac{\sqrt3}{3} ≈ 0.57735$
Inradius	$\frac{\sqrt3}{6} ≈ 0.28868$
Area	$\frac{3\sqrt3}{4} ≈ 1.29904$
Angle	60º
Central density	3
Number of external pieces	18
Level of complexity	2
Related polytopes
Army	En, edge length $\frac{2\sqrt3\sin\frac\pi9}{3}$
Dual	Fissal enneagram
Conjugate	None
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 fissal enneagram, or fen, is a polygon compound composed of 3 triangles. As such it has 9 edges and 9 vertices.

It is the second stellation of the enneagon.

Its quotient prismatic equivalent is the 9-3 step prism, which is four-dimensional.

Vertex coordinates

Coordinates for the vertices of a fissal enneagram of edge length 1 centered at the origin are given by:

• $\left(\frac{\sqrt3}{3},\,0\right),$
• $\left(\frac{\sqrt3\cos\frac{2\pi}{9}}{3},\,±\frac{\sqrt3\sin\frac{2\pi}{9}}{3}\right),$
• $\left(\frac{\sqrt3\cos\frac{4\pi}{9}}{3},\,±\frac{\sqrt3\sin\frac{4\pi}{9}}{3}\right),$
• $\left(-\frac{\sqrt3}{6},\,±\frac12\right),$
• $\left(\frac{\sqrt3\cos\frac{8\pi}{9}}{3},\,±\frac{\sqrt3\sin\frac{8\pi}{9}}{3}\right).$

External links

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