Grand hendecagram

Grand hendecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Gahn
Coxeter diagram	x11/5o ()
Schläfli symbol	{11/5}
Elements
Edges	11
Vertices	11
Vertex figure	Dyad, length 2cos(5π/11)
Measures (edge length 1)
Circumradius	$\frac{1}{2\sin\frac{5\pi}{11}} ≈ 0.50514$
Inradius	$\frac{11}{4\tan\frac{5\pi}{11}} ≈ 0.071889$
Area	$\frac{11}{4\tan\frac{5\pi}{11}} ≈ 0.39539$
Angle	$\frac{\pi}{11} ≈ 16.36364^\circ$
Central density	5
Number of external pieces	22
Level of complexity	2
Related polytopes
Army	Heng, edge length $2\cos\frac{5\pi}{11}$
Dual	Grand hendecagram
Conjugates	Hendecagon, small hendecagram, hendecagram, great 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 grand hendecagram is a non-convex polygon with 11 sides. It's created by taking the fourth stellation of a hendecagon. A regular grand 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 great hendecagram.

Vertex coordinates

Coordinates for a grand hendecagram of edge length 2sin(5π/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".