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| Regular nonagon | |
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| Edges and vertices | 9 |
| Schläfli symbols | {9} |
| Coxeter–Dynkin diagrams |    |
| Symmetry group | Dihedral (D9) |
| Area (with t=edge length |
  |
| 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
Although a regular nonagon is not constructible with compass and straightedge there are methods of constructing that are very close approximations.
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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
- Properties of a Nonagon (with interactive animation)
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