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 Z
- 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!
Not bad, eh?