One or more interior angles greater than 180°. Some vertices push 'inwards'
towards the interior of the polygon. The opposite of convex.
See Concave Polygons
Self-intersecting or Crossed
A polygon where one or more sides crosses back over another side, creating multiple smaller polygons. Most of the properties and theorems concerning polygons do not apply to this shape.
It is best considered as several separate polygons.
A polygon that in not self-intersecting in this way is called a simple polygon.
Properties of all Polygons (regular and irregular)
Many polygons have names based on the number of sides. A 5-sided polygon is called a pentagon for example.
There are some that wish to name every possible polygon, but there seems little point in doing so.
For example a 42-sided polygon is called a "tetracontakaidigon".
Beyond about 10 sides, most people call them an "n-gon". For example a 15-gon has 15 sides. This seems easier to remember and understand.
However, there are some names that do occur in everyday experience: