Hendecagon

Regular hendecagon
Edges and vertices	11
Schläfli symbols	{11}
Coxeter–Dynkin diagrams	Error creating thumbnail: Error creating thumbnail: Error creating thumbnail:
Symmetry group	Dihedral (D11)
Area (with $a$ = edge length)	$A=\frac{11}{4}\cot\left(\frac{\pi}{11}\right)a^2$$\simeq 9.36a^2$
Internal angle (degrees)	180°×(1-2/11) =147°.27

In geometry, a hendecagon (also undecagon) is an 11-sided polygon. The name "undecagon" is often seen as incorrect, but the matter is up for debate. The Greek prefix 'hen', is preferable to the Latin 'uni' or 'un'. A regular hendecagon has internal angles of 147.27 degrees. The area of a regular hendecagon with side length $a$ is given by

$A=\frac{11}{4}\cot\left(\frac{\pi}{11}\right)a^2\simeq9.36a^2$

A regular hendecagon is not constructible with compass and straightedge.

Use in coinage

The Canadian dollar coin, the loonie, is patterned on 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.

See also

• Hendecagram

Related shapes

The hendecagon shares the same set of 11 vertices with four regular hendecagrams, {11/2}, {11/3}, {11/4}, {11/5}.

Petrie polygons

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

File:10-simplex t0.svg 10-simplex

File:10-simplex t1.svg Rectified 10-simplex

Error creating thumbnail: Birectified 10-simplex

File:10-simplex t3.svg Trirectified 10-simplex

Quadrirectified 10-simplex

External links

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

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