# Great hendecagram

Great hendecagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGhen
Coxeter diagramx11/4o (     )
Schläfli symbol{11/4}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\frac{4\pi}{11}} ≈ 0.54967$ Inradius$\frac{11}{4\tan\frac{4\pi}{11}} ≈ 0.22834$ Area$\frac{11}{4\tan\frac{4\pi}{11}} ≈ 1.25588$ Angle$\frac{3\pi}{11} ≈ 49.09091^\circ$ Central density4
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length $\frac{\sin\frac{\pi}{11}}{\sin\frac{4\pi}{11}}$ DualGreat hendecagram
ConjugatesHendecagon, small hendecagram, hendecagram, grand hendecagram
Convex coreHendecagon
Abstract & topological properties
Flag count22
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11), order 22
ConvexNo
NatureTame

The great hendecagram is a non-convex polygon with 11 sides. It's created by taking the third stellation of a hendecagon. A regular great hendecagram has equal sides and equal angles.

It is one of four regular 11-sided star polygons, the other three being the small hendecagram, the hendecagram, and the grand hendecagram.

## Vertex coordinates

Coordinates for a great hendecagram of edge length 2sin(4π/11), centered at the origin, are:

• (1, 0),
• (cos(2π/11), ±sin(2π/11)),
• (cos(4π/11), ±sin(4π/11)),
• (cos(6π/11), ±sin(6π/11)),
• (cos(8π/11), ±sin(8π/11)),
• (cos(10π/11), ±sin(10π/11)).