# Grand hendecagram

Grand hendecagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGahn
Coxeter diagramx11/5o (     )
Schläfli symbol{11/5}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\frac{5\pi}{11}} ≈ 0.50514$ Inradius$\frac{11}{4\tan\frac{5\pi}{11}} ≈ 0.071889$ Area$\frac{11}{4\tan\frac{5\pi}{11}} ≈ 0.39539$ Angle$\frac{\pi}{11} ≈ 16.36364^\circ$ Central density5
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length $2\cos\frac{5\pi}{11}$ DualGrand hendecagram
ConjugatesHendecagon, small hendecagram, hendecagram, great hendecagram
Convex coreHendecagon
Abstract & topological properties
Flag count22
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11), order 22
ConvexNo
NatureTame

The grand hendecagram is a non-convex polygon with 11 sides. It's created by taking the fourth stellation of a hendecagon. A regular grand 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 great hendecagram.

## Vertex coordinates

Coordinates for a grand hendecagram of edge length 2sin(5π/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)).