# Small hendecagram

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

The small hendecagram, or shen, 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), ±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)).