# Hendecagram

Hendecagram Rank2
TypeRegular
SpaceSpherical
Bowers style acronymHenge
Info
Coxeter diagramx11/3o
Schläfli symbol{11/3}
SymmetryI2(11), order 22
ArmyHeng
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\frac{3\pi}{11}} ≈ 0.66159$ Inradius$\frac{1}{2\tan\frac{3\pi}{11}} ≈ 0.43325$ Area$\frac{11}{4\tan\frac{3\pi}{11}} ≈ 2.38289$ Angle$\frac{5\pi}{11} ≈ 81.81818°$ Central density3
Euler characteristic0
Number of pieces22
Level of complexity2
Related polytopes
DualHendecagram
ConjugatesHendecagon, small hendecagram, great hendecagram, grand hendecagram
Convex coreHendecagon
Properties
ConvexNo
OrientableYes
NatureTame

The hendecagram, or henge, also called the medial hendecagram, is a non-convex polygon with 11 sides. It's created by taking the second stellation of a hendecagon. A regular 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 great hendecagram, and the grand hendecagram. The name "hendecagram" is often used to describe any of these shapes.

## Vertex coordinates

Coordinates for a hendecagram of edge length 2sin(3π/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)).