Hendecagram

Hendecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Henge
Coxeter diagram	x11/3o ()
Schläfli symbol	{11/3}
Elements
Edges	11
Vertices	11
Vertex figure	Dyad, length 2cos(3π/11)
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	$\frac{5\pi}{11} ≈ 81.81818^\circ$
Central density	3
Number of external pieces	22
Level of complexity	2
Related polytopes
Army	Heng, edge length $\frac{\sin\frac{\pi}{11}}{\sin\frac{3\pi}{11}}$
Dual	Hendecagram
Conjugates	Hendecagon, small hendecagram, great 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 hendecagram 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

The vertex coordinates for a hendecagram are the same as those of the hendecagon.

External links

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

• Wikipedia Contributors. "Hendecagram".