Nonagon
| Regular nonagon (enneagon) | |
|---|---|
 A regular nonagon (enneagon) |
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| Type | Regular polygon |
| Edges and vertices | 9 |
| Schläfli symbol | {9} |
| Coxeter diagram |    |
| Symmetry group | Dihedral (D9), order 2×9 |
| Internal angle (degrees) | 140° |
| Dual polygon | self |
| Properties | convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, a nonagon pron.: /ˈnɒnəɡɒn/ (or enneagon /ˈɛniːəɡɒn/) is a nine-sided regular polygon.
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.
A regular nonagon has internal angles of 140°. The area of a regular nonagon of side length a is given by
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Construction [edit]
Although a regular nonagon is not constructible with compass and straightedge there are methods of construction that produce very close approximations.
Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
Graphs [edit]
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:
 8-simplex (8D) |
 Rectified 8-simplex (8D) |
 Birectified 8-simplex (8D) |
 Trirectified 8-simplex (8D) |
Pop culture references [edit]
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] Slipknot's logo is also a version of a nonagon, being a nine-pointed star made of 3 triangles.
Architecture [edit]
Temples of Baha'i Faith are required to be nonagonal.
See also [edit]
- Enneagram (nonagram)
References [edit]
External links [edit]
- Properties of a Nonagon (with interactive animation)
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