# Compound of three triangles

(Redirected from Fissal enneagram)
Compound of three triangles
Rank2
TypeRegular
Notation
Bowers style acronymFen
Schläfli symbol{9/3}
Elements
Components3 triangles
Edges9
Vertices9
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {3}}{3}}\approx 0.57735}$
Inradius${\displaystyle {\frac {\sqrt {3}}{6}}\approx 0.28868}$
Area${\displaystyle {\frac {3{\sqrt {3}}}{4}}\approx 1.29904}$
Angle60º
Central density3
Number of external pieces18
Level of complexity2
Related polytopes
ArmyEn, edge length ${\displaystyle {\frac {2{\sqrt {3}}\sin {\frac {\pi }{9}}}{3}}}$
DualCompound of three triangles
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:

• ${\displaystyle \left({\frac {\sqrt {3}}{3}},\,0\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {2\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {2\pi }{9}}}{3}}\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {4\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {4\pi }{9}}}{3}}\right),}$
• ${\displaystyle \left(-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {8\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {8\pi }{9}}}{3}}\right).}$