# Small hendecagram

Small hendecagram
Rank2
TypeRegular
Notation
Bowers style acronymShen
Coxeter diagramx11/2o ()
Schläfli symbol{11/2}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {2\pi }{11}}}}\approx 0.92483}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {2\pi }{11}}}}\approx 0.77802}$
Area${\displaystyle {\frac {11}{4\tan {\frac {2\pi }{11}}}}\approx 4.27908}$
Angle${\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}$
Central density2
Number of external pieces22
Level of complexity2
Related polytopes
ArmyHeng, edge length ${\displaystyle {\frac {1}{2\cos {\frac {\pi }{11}}}}}$
DualSmall hendecagram
ConjugatesHendecagon, hendecagram, great hendecagram, grand hendecagram
Convex coreHendecagon
Abstract & topological properties
Flag count22
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11), order 22
ConvexNo
NatureTame

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

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

## Vertex coordinates

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