Decagon

The decagon, or dec, is a polygon with 10 sides. A regular decagon has equal sides and equal angles.

The combining prefix is da-, as in dadip.

The only non-compound stellation of the decagon is the decagram. The only other polygons with a single non-compound stellation are the pentagon, the octagon, and the dodecagon.

Vertex coordinates
Coordinates for a decagon of unit edge length, centered at the origin are all sign changes of:


 * (±1/2, ±$\sqrt{(5+√5)/2}$/2),
 * (±(3+$\sqrt{5}$)/4, ±$\sqrt{5+2√5}$),
 * (±(1+$\sqrt{(5+2√5)}$)/2, 0).

Representations
A regular decagon can be represented by the following Coxeter diagrams:


 * x10o (regular),
 * x5x (H2 symmetry, generally a dipentagon),
 * to5ot&#zx (t=$\sqrt{(5+2√5)}$, generally a pentambus),
 * xFV Tto&#zx (rectangular symmetry, t as above, T=ft),
 * xFVFx&#xt (axial edge-first),
 * otTTto&#xt (axial vertex-first).

Dipentagon
A dipentagon is a variant decagon with pentagonal symmetry, formed as a truncated pentagon. When decagons appear as faces in higher polytopes, they usually have this symmetry. Its dual is the pentambus.

Stellations

 * 1st stellation: Stellated decagon (compound of two pentagons)
 * 2nd stellation: Decagram
 * 3rd stellation: Stellated decagram (compound of two pentagrams)