Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
Polygons are 2dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).
Polygon (straight sides) 
Not a Polygon (has a curve) 
Not a Polygon (open, not closed) 
Polygon comes from Greek. Poly means "many" and gon means "angle".
Types of Polygons
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
Regular  Irregular 
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)
Convex  Concave 
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex.
Simple Polygon (this one's a Pentagon) 
Complex Polygon (also a Pentagon) 
More Examples
Irregular Hexagon 
Concave Octagon 
Complex Polygon (a "star polygon", in this case a pentagram) 
Play With Them!Try Interactive Polygons ... make them regular, concave or complex. 
Names of Polygons
If it is a Regular Polygon...  
Name  Sides  Shape  Interior Angle 

Triangle (or Trigon)  3  60°  
Quadrilateral (or Tetragon)  4  90°  
Pentagon  5  108°  
Hexagon  6  120°  
Heptagon (or Septagon)  7  128.571°  
Octagon  8  135°  
Nonagon (or Enneagon)  9  140°  
Decagon  10  144°  
Hendecagon (or Undecagon)  11  147.273°  
Dodecagon  12  150°  
Triskaidecagon  13  152.308° 

Tetrakaidecagon  14  154.286° 

Pentadecagon  15  156° 

Hexakaidecagon  16  157.5° 

Heptadecagon  17  158.824° 

Octakaidecagon  18  160° 

Enneadecagon  19  161.053° 

Icosagon  20  162° 

Triacontagon  30  168° 

Tetracontagon  40  171° 

Pentacontagon  50  172.8° 

Hexacontagon  60  174° 

Heptacontagon  70  174.857° 

Octacontagon  80  175.5° 

Enneacontagon  90  176° 

Hectagon  100  176.4° 

Chiliagon  1,000  179.64° 

Myriagon  10,000  179.964° 

Megagon  1,000,000  ~180°  
Googolgon  10^{100}  ~180°  
ngon  n  (n2) × 180° / n 
You can make names using this method:



Example: a 62sided polygon is a Hexacontadigon 
BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13gon", "14gon" ... "100gon", etc.