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

Many More

Animated Polyhedron Models  

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