# Fissal enneagram

Fissal enneagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymFen
Schläfli symbol{9/3}
Elements
Components3 triangles
Edges9
Vertices9
Measures (edge length 1)
Circumradius$\frac{\sqrt3}{3} ≈ 0.57735$ Inradius$\frac{\sqrt3}{6} ≈ 0.28868$ Area$\frac{3\sqrt3}{4} ≈ 1.29904$ Angle60º
Central density3
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length $\frac{2\sqrt3\sin\frac\pi9}{3}$ DualFissal enneagram
ConjugateNone
Convex coreEnneagon
Abstract & topological properties
Flag count18
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9), order 18
ConvexNo
NatureTame

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:

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