Polyhedrons

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

So, to be a polyhedron there should be no curved surfaces.

Examples of Polyhedra:

Triangular Prism	Cube	Dodecahedron

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

If you count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron, you can 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 you 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