Polygons

A polygon is a plane shape with straight sides.

Is it a Polygon?

Polygons are 2-dimensional 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 10100   ~180°
n-gon n (n-2) × 180° / n

You can make names using this method:

Sides
  Start with...
20
  Icosi...
30
  Triaconta...
40
  Tetraconta...
50
  Pentaconta...
60
  Hexaconta...
70
  Heptaconta...
80
  Octaconta...
90
  Enneaconta...
100   Hecta...
etc..    
Sides
  ...end with
+1
  ...henagon
+2
  ...digon
+3
  ...trigon
+4
  ...tetragon
+5
  ...pentagon
+6
  ...hexagon
+7
  ...heptagon
+8
  ...octagon
+9
  ...enneagon

Example: a 62-sided polygon is a Hexacontadigon

BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100-gon", etc.