Nonagon
| Regular nonagon | |
|---|---|
A regular nonagon |
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| Edges and vertices | 9 |
| Schläfli symbol | {9} |
| Coxeter–Dynkin diagrams | |
| Symmetry group | Dihedral (D9) |
| Internal angle (degrees) | 140° |
| Properties | convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, a nonagon /ˈnɒnəɡɒn/ (or enneagon /ˈɛniːəɡɒn/) is a nine-sided 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
Contents |
Construction
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
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. 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
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]
See also
- Enneagram (nonagram)
References
- Weisstein, Eric W., "Nonagon" from MathWorld.
External links
- Properties of a Nonagon (with interactive animation)
- Nonagrams
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