# Hendecagon

Hendecagon Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymHeng
Coxeter diagramx11o (   )
Schläfli symbol{11}
Elements
Edges11
Vertices11
Measures (edge length 1)
Circumradius$\frac{1}{2\sin\left(\frac{\pi}{11}\right)}≈ 1.77473$ Inradius$\frac{1}{2\tan\left(\frac{\pi}{11}\right)} ≈ 1.70284$ Area$\frac{11}{4\tan\left(\frac{\pi}{11}\right)} ≈ 9.36564$ Angle$\frac{9\pi}{11} ≈ 147.27273^\circ$ Central density1
Number of pieces11
Level of complexity1
Related polytopes
ArmyHeng
DualHendecagon
ConjugatesSmall hendecagram, hendecagram, great hendecagram, grand hendecagram
Abstract properties
Flag count22
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryI2(11), order 22
ConvexYes
NatureTame

The hendecagon is a polygon with 11 sides. A regular hendecagon has equal sides and equal angles.

The combining prefix in BSAs is hen-, as in hentet, or han-, as in handip.

It has four stellations, these being the small hendecagram, the hendecagram, the great hendecagram, and the grand hendecagram.

It is the smallest regular convex polygon that cannot form a planar vertex with only other regular convex polygons.

Higher polytopes containing regular hendecagons that are "interesting" in some sense are rare. An exception is three members of the family of pairwise augmented cupolae, which are 11-4-3 acrohedra (all faces are regular).

## Naming

The name hendecagon is derived from the Ancient Greek ἕνδεκα (11) and γωνία (angle), referring to the number of vertices.

Other names include:

• heng, Bowers style acronym, short for "hendecagon"

## Vertex coordinates

Vertex coordinates for a hendecagon of edge length $2\sin(\pi/11)$ , centered at the origin, are:

• $(1,\,0)$ ,
• $(\cos(2\pi/11),\,\pm\sin(2\pi/11))$ ,
• $(\cos(4\pi/11),\,\pm\sin(4\pi/11))$ ,
• $(\cos(6\pi/11),\,\pm\sin(6\pi/11))$ ,
• $(\cos(8\pi/11),\,\pm\sin(8\pi/11))$ ,
• $(\cos(10\pi/11),\,\pm\sin(10\pi/11))$ .