Dodecagon

The dodecagon, or dog, is a polygon with 12 sides. A regular dodecagon has equal sides and equal angles.

The combining prefix is twa-, as in twaddip.

The only non-compound stellation of the dodecagon is the dodecagram. This makes it the largest polygon with a single non-compound stellation. The only other polygons with only one are the pentagon, the octagon, and the decagon.

Naming
The name decagon is derived from the Ancient Greek δώδεκα (12) and γωνία (angle), referring to the number of vertices.

Other names include:


 * dog, Bowers style acronym, short for "dodecagon"

Vertex coordinates
Coordinates for a dodecagon of unit edge length, centered at the origin, are all permutations of:


 * (±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{6}$)/2),
 * (±1/2, ±(2+$\sqrt{2}$)/2).

Representations
A dodecagon has the following Coxeter diagrams:


 * x12o (full symmetry)
 * x6x (G2 symmetry, generally a dihexagon)
 * xy3yx&#zx (A2 symmetry, y = 1+√3)

Dihexagon
A dihexagon is a variant dodecagon with hexagon symmetry, form as a truncated hexagon. Dodecagons appearing in higher polytopes usually have this symmetry. Its dual is the hexambus.

Stellations

 * 1st stellation: Stellated dodecagon (compound of two hexagons)
 * 2nd stellation: Trisquare (compound of three squares)
 * 3rd stellation: Tetratriangle (compound of four triangles)
 * 4th stellation: Dodecagram