Great hendecagram

Great hendecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Ghen
Coxeter diagram	x11/4o ()
Schläfli symbol	{11/4}
Elements
Edges	11
Vertices	11
Vertex figure	Dyad, length 2cos(4π/11)
Measures (edge length 1)
Circumradius	$\frac{1}{2\sin\frac{4\pi}{11}} ≈ 0.54967$
Inradius	$\frac{11}{4\tan\frac{4\pi}{11}} ≈ 0.22834$
Area	$\frac{11}{4\tan\frac{4\pi}{11}} ≈ 1.25588$
Angle	$\frac{3\pi}{11} ≈ 49.09091^\circ$
Central density	4
Number of external pieces	22
Level of complexity	2
Related polytopes
Army	Heng, edge length $\frac{\sin\frac{\pi}{11}}{\sin\frac{4\pi}{11}}$
Dual	Great hendecagram
Conjugates	Hendecagon, small hendecagram, hendecagram, grand hendecagram
Convex core	Hendecagon
Abstract & topological properties
Flag count	22
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11), order 22
Convex	No
Nature	Tame

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)).

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

• Wikipedia Contributors. "Hendecagram".