|Regular nonagon (enneagon)|
A regular nonagon (enneagon)
|Edges and vertices||9|
|Symmetry group||Dihedral (D9), order 2×9|
|Internal angle (degrees)||140°|
|Properties||convex, cyclic, equilateral, isogonal, isotoxal|
The name "nonagon" is a prefix 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 than "nonagon".
A regular nonagon has internal angles of 140°. The area of a regular nonagon of side length a is given by
Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
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)
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. Slipknot's logo is also a version of a nonagon, being a nine-pointed star made of 3 triangles.
Temples of Baha'i Faith are required to be nonagonal.
The U.S. Steel Tower is an irregular nonagon.
- Enneagram (nonagram)
- Properties of a Nonagon (with interactive animation)