Numerous regular polygons may be seen in nature.

In the world of geology, crystals have flat faces, or facets, which are polygons.

The most famous hexagons in nature are found in the animal kingdom. The wax honeycomb made by bees is an array of hexagons used to store honey and pollen, and as a secure place for the larvae to grow.

Moving off the earth into space, early mathematicians doing calculations using Newton's law of gravitation discovered that if two bodies (such as the sun and the earth) are orbiting one another, there exist certain points in space, called Lagrangian points, where a smaller body (such as an asteroid or a space station) will remain in a stable orbit. The sun-earth system has five Lagrangian points.

~Lagrangian points form an equilateral triangle.

Another dynamic example of regular polygons occurs when the cooling of lava forms areas of tightly packed hexagonal columns of basalt, which may be seen at the Giant's Causeway in Ireland, or at the Devil's Postpile in California.

A polygon is CONVEX if no line containing any side of the polygon contains points in its INTERIOR.

An additional way to view convexity is by considering an arbitrary line as it cuts through the interior of the polygon. If the line moves repeatedly from exterior to interior the polygon is concave (not convex).

An additional way to view convexity is by considering an arbitrary line as it cuts through the interior of the polygon. If the line moves repeatedly from exterior to interior the polygon is concave (not convex).