## Friday, October 1, 2010

### Speaking of Cuboid Complex Polyhedrons

We start working with geometric shapes in elementary math, and their descriptions and dimensions are a bit simpler than those of a fat car (about which we spoke yesterday).

For example, here's a rectangular prism. Also known as a box to most of us. But to mathematicians, it's also a cuboid, or convex polyhedron, or right rectangular hexahedron, or rectangular parallelepiped. And if those names aren't enough to scare you, it's shown here in unfolded and 3-dimensional forms.

(I drew this manually with my Illustrator software so please excuse me if the shapes are not perfect!)

There are 6 faces; each one is a rectangle. (Ignore the folding tabs.)  It has 12 edges and 8 vertices.

The long side is called the length, the vertical side the height, and the other side the width or depth.

You can draw a diagonal between any two non-adjacent vertices in a single plane (as shown by the red line) or a space diagonal line between any two non-adjacent vertices in space (as shown by the blue line).

Looking at the diagram, the dimensions X, Y and

- can be multiplied like this to get the volume:  X x Y x Z = Volume (given in cubic units)

- can be manipulated like this to get the surface area:  2XY + 2XZ + 2YZ = Surface Area (given in square units)

Take a whole bunch of little rectangular cuboid shapes like this, combine them together, and you can make almost anything, even a car with a wide track!