|Bowers style acronym||En|
|Symmetry||I2(9), order 18|
|Vertex figure||Dyad, length 2cos(π/9)|
|Measures (edge length 1)|
|Number of pieces||9|
|Level of complexity||1|
|Conjugates||Enneagram, great enneagram|
The enneagon or en, sometimes referred to as a nonagon, is a polygon with 9 sides. A regular enneagon has equal sides and equal angles.
The combining prefix is e-, as in edip.
Like heptagons, enneagons are generally rare in higher polytopes.
Naming[edit | edit source]
The name enneagon is derived from the Ancient Greek ἐννέα (9) and γωνία (angle), referring to the number of vertices.
Other names include:
- En, Bowers style acronym, short for "enneagon".
Vertex coordinates[edit | edit source]
Coordinates for an enneagon of edge length 2sin(π/9), centered at the origin, are:
- (1, 0),
- (cos(2π/9), ±sin(2π/9)),
- (cos(4π/9), ±sin(4π/9)),
- (–1/2, ±√/2),
- (cos(8π/9), ±sin(8π/9)).
Variations[edit | edit source]
Besides the regular enneagon, other enneagons with triangular, mirror, or no symmetry exist. A few higher polytopes, such as certain swirlchora, have trigon-symmetric enneagons as facces.
Stellations[edit | edit source]
- 1st stellation: Enneagram
- 2nd stellation: Fissal enneagram (compound of three triangles)
- 3rd stellation: Great enneagram
[edit | edit source]
- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".
- Wikipedia Contributors. "Nonagon".