Polygons

polygon mosaic
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).

pentagon irregularnot a pentagon (curve)not a pentagon (open)
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

A regular polygon has all angles equal and all sides equal, otherwise it is irregular

pentagon regular pentagon 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)

pentagon irregular pentagon concave
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.

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

 

More Examples

hexagon irregular concave octagon star polygon
Irregular Hexagon

 Concave Octagon

 Complex Polygon
(a "star polygon",
in this case a pentagram)

 

polygons interactive

Play With Them!

Try Interactive Polygons ... make them regular, concave or complex.

 

Names of Polygons

  If it is a Regular Polygon...
NameSidesShapeInterior Angle
Triangle (or Trigon)3regular triangle60°
Quadrilateral (or Tetragon)4regular quadrilateral90°
Pentagon5pentagon regular108°
Hexagon6hexagon regular120°
Heptagon (or Septagon)7heptagon refular128.571°
Octagon8octagon regular135°
Nonagon (or Enneagon) 9nonagon regular140°
Decagon10regular decagon144°
Hendecagon (or Undecagon)11regular hendecagon147.273°
Dodecagon12regular dodecagon150°
Triskaidecagon 13 152.308°
Tetrakaidecagon 14 154.286°
Pentadecagon15 156°
Hexakaidecagon 16 157.5°
Heptadecagon17 158.824°
Octakaidecagon 18 160°
Enneadecagon19 161.053°
Icosagon20 162°
Triacontagon30 168°
Tetracontagon 40 171°
Pentacontagon50 172.8°
Hexacontagon 60 174°
Heptacontagon 70 174.857°
Octacontagon 80 175.5°
Enneacontagon 90 176°
Hectagon100 176.4°
Chiliagon1,000 179.64°
Myriagon10,000 179.964°
Megagon1,000,000 ~180°
Googolgon10100 ~180°
n-gonnregular n gon(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..  
right arrow
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.

Remembering

Quadrilateral (4 Sides)

quad bike
A Quad Bike has 4 wheels

Pentagon (5 Sides)

pentagon building
The "Pentagon" in Washington DC has 5 sides

Hexagon (6 Sides)

honeycomb
Honeycomb has Hexagons

Septagon (7 Sides)

Think Septagon is a "Seven-agon"

Octagon (8 Sides)

octopus
An Octopus has 8 tentacles

Nonagon (9 Sides)

Think Nonagon is a "Nine-agon"

Decagon (10 Sides)

Think Decagon has 10 sides,
just like our Decimal system has 10 digits