 Eric W. Weisstein, Pentagon at MathWorld.
 How to construct a regular pentagon using only compass and straightedge
 Definition and properties of the pentagon, with interactive animation
 Nine constructions for the regular pentagon by Robin Hu
 Renaissance artists' approximate constructions of regular pentagons at Convergence
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Pentagon
A regular pentagon, {5}
Regular pentagon  

Edges and vertices  5 
Schläfli symbol  {5} 
Coxeter–Dynkin diagram  
Symmetry group  Dihedral (D_{5}) 
Area (with t=edge length) 

Internal angle (degrees) 
108° 
In geometry, a pentagon is any fivesided polygon. A pentagon may be simple or selfintersecting. The internal angles in a simple pentagon total 540°.
Regular pentagons
The term pentagon is commonly used to mean a regular convex pentagon, where all sides are equal and all interior angles are equal (to 108°). Its Schläfli symbol is {5}.
The area of a regular convex pentagon with side length t is given by
A pentagram is a regular star pentagon. Its Schläfli symbol is {5/2}. Its sides form the diagonals of a regular convex pentagon  in this arrangement the sides of the two pentagons are in the golden ratio.
Construction
A regular pentagon is constructible using a compass and straightedge, either by inscribing one in a given circle or constructing one on a given edge. This process was described by Euclid in his Elements circa 300 BC.
One method to construct a regular pentagon in a given circle is as follows:
Construction of a regular pentagon
1. Draw a circle in which to inscribe the pentagon and mark the center point O. (This is the green circle in the diagram to the right).
2. Choose a point A on the circle that will serve as one vertex of the pentagon. Draw a line through O and A.
3. Construct a line perpendicular to the line OA passing through O. Mark its intersection with one side of the circle as the point B.
4. Construct the point C as the midpoint of O and B.
5. Draw a circle centered at C through the point A. Mark its intersection with the line OB (inside the original circle) as the point D.
6. Draw a circle centered at A through the point D. Mark its intersections with the original (green) circle as the points E and F.
7. Draw a circle centered at E through the point A. Mark its other intersection with the original circle as the point G.
8. Draw a circle centered at F through the point A. Mark its other intersection with the original circle as the point H.
9. Construct the regular pentagon AEGHF.
Constructing a pentagon
After forming a regular convex pentagon, if you join the nonadjacent corners (drawing the diagonals of the pentagon), you obtain a pentagram, with a smaller regular pentagon in the center. Or if you extend the sides until the nonadjacent ones meet, you obtain a larger pentagram.
Links
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
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