Introduction

If you've already taken a basic geometry course then I want you to think back to that course and remember all of those extremely interesting shapes you learned about, circles, squares, triangles, and all of those other shapes. Now I want you to think about what was wrong with all of those shapes. Give up? They are all two dimensional, and believe it or not the world is three dimensional (if you don't believe me then check). This web page will give you a brief glimpse at GEOMETRY IN 3D (sounds like an old B-Grade movie, doesn't it).

When we talked about polygons in our old geometry classes we were referring to two dimensional shapes. Now that we're talking about three dimensional shapes we use a different term, polyhedra. A polyhedra is any three dimensional shape made up flat surfaces.

When we talked about Polygons we used two axis in our Cartesian Coordinate System. When talking about Polyhedra another axis is added, the Z axis. The Z axis runs through the Origin toward you.

All polyhedra are made with combinations of polygons. A cube, for example, is made up of six squares.

In order for the polygons to come together and fit into a polyhedra several conditions must be met. First, there must be at least three shapes joining at each point. If you have any less, your polyhedra wouldn't be three dimensional. Second, the angles of all the polygons which connect at a point must be less then 360 degrees. In order to understand the last one, picture a cube in you head (or look at the shape above) every vertex of the cube is touching three squares. Now try picturing a shape with four squares at each vertex. What you get is just a plane, or a flat, two-dimensional surface. You can't use four squares like this to create a polyhedra. The reason is each angle of a square is 90 degrees. If you were to put three squares together their angles would add up to 270 (90 x 3) degrees. If you were to put four squares their angles add up to 360 (90 x 4) degrees. 270 is less then 360 degrees, but the 360 degrees from the four squares isn't less then the 360 degree limit. It's exactly equal to it, which doesn't work. If you tried 5 squares the total would be 450 degrees, which is way over 360 so that wouldn't work either.

Return to the main page.