Enneagon

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 regular heptagons, regular enneagons are rarely found in higher polytopes that are objects of study, as they do not occur any non-prismatic uniform polyhedra or Johnson solids. A notable exception is the pairwise augmented cupolas, which are acrohedra. Enneagons also appear in some near-miss Johnson solids, such as the sesquitruncated octahedron.

Naming
The name enneagon is derived from the Ancient Greek ' (9) and ' (angle), referring to the number of vertices.

Other names include:


 * En, Bowers style acronym, short for "enneagon".

Vertex coordinates
Coordinates for an enneagon of edge length $$2\sin(\pi/9)$$, centered at the origin, are:


 * $$(1, 0)$$,
 * $$(\cos(2\pi/9), \pm\sin(2\pi/9))$$,
 * $$(\cos(4\pi/9), \pm\sin(4\pi/9))$$,
 * $$(–1/2, \pm\sqrt{3}/2)$$,
 * $$(\cos(8\pi/9), \pm\sin(8\pi/9))$$.

Variations
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

 * 1st stellation: Enneagram
 * 2nd stellation: Fissal enneagram (compound of three triangles)
 * 3rd stellation: Great enneagram