Hendecagon

Regular hendecagon
A regular hendecagon
Type	Regular polygon
Edges and vertices	11
Schläfli symbol	{11}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D11)
Internal angle (degrees)	$\approx 147.273$°
Properties	convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a hendecagon (also undecagon) is an 11-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and gon– "corner", is often preferred to the hybrid undecagon, whose first syllable un– is Latin for "one".)

Regular hendecagon

A regular hendecagon has internal angles of 147.27 degrees. The area of a regular hendecagon with side length a is given by

$A = \frac{11}{4}a^2 \cot \frac{\pi}{11} \simeq 9.36564\,a^2.$

A regular hendecagon is not constructible with compass and straightedge.

Use in coinage

The Canadian dollar coin, the loonie, is similar to, but not exactly, a regular hendecagonal prism, as is the Indian two-rupee coin.

It was also patterned on the Susan B. Anthony dollar of the United States from 1979–1981 and again in 1999 and Sri Lanka 10 Rupees 2009.

Hendecagrams

The hendecagon is the perimeter of four regular hendecagrams, {11/2}, {11/3}, {11/4}, {11/5}.

Construction

A regular hendecagon cannot be constructed using compass and straightedge. Because 11 is not a Pierpont prime, construction of a regular hendecagon is still impossible even with the usage of an angle trisector.

Petrie polygons

The regular hendecagon is the Petrie polygon for 10-dimensional uniform polytopes of the simplex family, projected in a skew orthogonal projection.

10-simplex

Rectified 10-simplex

Birectified 10-simplex

Trirectified 10-simplex

Quadrirectified 10-simplex

External links

• Properties of an Undecagon (hendecagon) With interactive animation
• Weisstein, Eric W., "Hendecagon" from MathWorld.