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
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 |
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