# Great hendecagram

Great hendecagram
Rank2
TypeRegular
Notation
Bowers style acronymGhen
Coxeter diagramx11/4o ()
Schläfli symbol{11/4}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {4\pi }{11}}}}\approx 0.54967}$
Inradius${\displaystyle {\frac {11}{4\tan {\frac {4\pi }{11}}}}\approx 0.22834}$
Area${\displaystyle {\frac {11}{4\tan {\frac {4\pi }{11}}}}\approx 1.25588}$
Angle${\displaystyle {\frac {3\pi }{11}}\approx 49.09091^{\circ }}$
Central density4
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length ${\displaystyle {\frac {\sin {\frac {\pi }{11}}}{\sin {\frac {4\pi }{11}}}}}$
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)).