# Grand hendecagram

Grand hendecagram
Rank2
TypeRegular
Notation
Bowers style acronymGahn
Coxeter diagramx11/5o ()
Schläfli symbol{11/5}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {5\pi }{11}}}}\approx 0.50514}$
Inradius${\displaystyle {\frac {11}{4\tan {\frac {5\pi }{11}}}}\approx 0.071889}$
Area${\displaystyle {\frac {11}{4\tan {\frac {5\pi }{11}}}}\approx 0.39539}$
Angle${\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}$
Central density5
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length ${\displaystyle 2\cos {\frac {5\pi }{11}}}$
DualGrand hendecagram
ConjugatesHendecagon, small hendecagram, hendecagram, great hendecagram
Convex coreHendecagon
Abstract & topological properties
Flag count22
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11), order 22
Flag orbits1
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), \pmsin(2π/11)),
• (cos(4π/11), \pmsin(4π/11)),
• (cos(6π/11), \pmsin(6π/11)),
• (cos(8π/11), \pmsin(8π/11)),
• (cos(10π/11), \pmsin(10π/11)).