Nonagon

Regular nonagon
Edges and vertices	9
Schläfli symbols	{9}
Coxeter–Dynkin diagrams	Image:CDW ring.pngImage:CDW 9.pngImage:CDW dot.png
Symmetry group	Dihedral (D9)
Area (with t=edge length	Failed to parse (Missing texvc executable; please see math/README to configure.): A = \frac{9}{4}t^2\cot\frac{\pi}{9} Failed to parse (Missing texvc executable; please see math/README to configure.): \simeq6.18182t^2
Internal angle (degrees)	140°

In geometry, a nonagon (or enneagon) is a nine-sided polygon.

The name "nonagon" is a hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon, (εννεα, nine + γωνον, corner), and is arguably more correct, though somewhat less common.

A regular nonagon has internal angles of 140°. The area of a regular nonagon of side length a is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): A = \frac{9}{4}a^2\cot\frac{\pi}{9}\simeq6.18182a^2

Although a regular nonagon is not constructible with compass and straightedge there are methods of constructing that are very close approximations.

Graphs and stars

The K₉ complete graph is often drawn as a regular nonagon with all 36 edges connected. This graph also represents an orthographic projection of the 9 vertices and 36 edges of the 8-simplex.

Image:Complete graph K9.svg

The regular nonagon also contains 3 star figures, the third being the compound of three equilateral triangles:

Image:Star polygon 9 2.pngImage:Star polygon 9 4.pngImage:Star figure 9-3.png

OK

References

• Eric W. Weisstein, Nonagon at MathWorld.

External links

• Properties of a Nonagon With interactive animation

cs:Devítiúhelník

de:Neuneck es:Eneágono gl:Eneágono ja:九角形 hu:Kilencszög no:Enneagon pl:Dziewięciokąt pt:Eneágono sr:Деветоугао fi:Yhdeksänkulmio th:รูปเก้าเหลี่ยม