# Polyhedrons

A polyhedron is a solid with flat faces
(from Greek poly- meaning "many" and -edron meaning "face").

Each face is a polygon (a flat shape with straight sides).

So: no curved surfaces!

## Examples of Polyhedra:

Cube Triangular Prism Dodecahedron Its faces are all squares Its faces are triangles and rectangles What faces does it have?

## Common Polyhedra

 Platonic Solids Prisms Pyramids

## Many More

 Explore 100s of Animated Polyhedron Models. You can also see some Images of Polyhedra if you want.

## Counting Faces, Vertices and Edges

When we count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron we discover an interesting thing:

The number of faces plus the number of vertices
minus the number of edges equals 2

This can be written neatly as a little equation:

### F + V − E = 2

It is known as Euler's Formula (or the "Polyhedral Formula") and is very useful to make sure we have counted correctly!

### Let's try some examples:

 This cube has: 6 Faces 8 Vertices (corner points) 12 Edges F + V − E = 6 + 8 − 12 = 2

 This prism has: 5 Faces 6 Vertices (corner points) 9 Edges F + V − E = 5 + 6 − 9 = 2

But there are cases where it does not work! Read Euler's Formula for more.

Note: the plural of polyhedron is either polyhedrons or polyhedra