Enneagon

All you want to know about Enneagon

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		 A = \frac{9}{4}t^2\cot\frac{\pi}{9} \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 (from γωνία = 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

A = \frac{9}{4}a^2\cot\frac{\pi}{9}\simeq6.18182\,a^2.

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

Contents

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.

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

Pop culture references

They Might Be Giants have a song entitled "Nonagon" on their children's album "Here Come the 123s." It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.[1]

References

External links

v • d • e
Polygons
Listed by number of sides
1-10 sides
Henagon (Monogon) · Digon · Triangle (Trigon) · Quadrilateral (Tetragon) · Pentagon · Hexagon  · Heptagon  · Octagon  · Nonagon (Enneagon)  · Decagon
11-20 sides
Retrieved from "http://en.wikipedia.org/wiki/Nonagon"

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