Stage Two: Polygons and Polyhedrons

Polygons

After teaching the building blocks of geometry, I like to focus on polygons and polyhedrons. A polygon is a simple, closed curve with sides that are line segments. What are simple and closed curves?

Simple curve = a curve that does not cross itself

Closed curve = a curve that starts and stops at the same point

Here are examples of polygons and the number of sides they have:

With polygons, we also look at convex and concave curves:

Convex curves are simple, closed curves such that the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve. Concave curves are simple, closed curves that are not convex meaning that it is possible for a line segment connecting two interior points to cross outside the interior of the curve.

Polyhedra

A polyhedron is a simple closed surface made up of polygonal regions, or faces. Faces are flat surfaces that forms part of the boundary of an object. Vertices are the points an object has and edges are particular line segments that join the vertices.

To find the relationship between these parts of a polyhedron, we use the formula:

VERTICES + FACES - EDGES = 2 or V + F - E = 2

WEBSITE: http://world.mathigon.org/Polygons_and_Polyhedra