|Edges and vertices||9|
|Symmetry group||Dihedral (D9)|
(with t=edge length
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.
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.
- Weisstein, Eric W., "Nonagon" from MathWorld.
The K9 complete graph is often drawn as a regular enneagon with all 36 edges connected. This graph also represents an orthographic projection of the 9 vertices and 36 edges of the 8-simplex. Three other rectified forms also project inside of a regular enneagon:
Rectified 8-simplex (8D)
Birectified 8-simplex (8D)
Trirectified 8-simplex (8D)
- Properties of a Nonagon (with interactive animation)
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