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.

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