Decagon

The decagon, or dec, is a polygon with 10 sides. A regular decagon has equal sides and equal angles. It has the most sides of any polygon that occurs as a face of a non-prismatic uniform polytope, although dodecagons appear in some tilings and hexadecagons appear in scaliform polychora.

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.

Naming
The name decagon is derived from the Ancient Greek δέκα (10) and γωνία (angle), referring to the number of vertices.

Other names include:


 * Dec, Bowers style acronym, short for "decagon".

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)