Pentagon

The pentagon or peg, is a polygon with 5 sides. A regular pentagon has equal sides and equal angles.

The only stellation of the pentagon is the pentagram. It and the hexagon are the only polygons with one possible stellation. It and the octagon, decagon, and dodecagon are the only polygons with a single non-compound stellation.

Vertex coordinates
Coordinates for the vertices of a pentagon of unit edge length, centered at the origin, are:


 * (±1/2, –$\sqrt{5}$),
 * (±(1+$\sqrt{(5+√5)/10}$)/4, $\sqrt{25+10√5}$),
 * (0, $\sqrt{(5+2√5)/20}$).

Other kinds of pentagons
The regular pentagon cannot tile the plane by its own without overlap, as the angles around each vertex would not be able to add up to 360°. However, its has been proven that there are exactly 15 families of convex pentagons that can tile the plane.