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)

Types of Polygons

Simple or Complex

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!

Simple Polygon (this one's a Pentagon)	Complex Polygon (also a Pentagon)

Concave or Convex

A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.

If there are any internal angles greater than 180° then it is concave. (Think: concave has a "cave" in it)

Convex	Concave

Regular or Irregular

If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular

Regular	Irregular

More Examples

Complex Polygon (a "star polygon", in this case, a pentagram)	Concave Octagon	Irregular Hexagon

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

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