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).

Examples of Polyhedra:

Its faces are all squares
triangular prismTriangular Prism
Its faces are triangles
and rectangles
What faces does it have?

So no curved surfaces: cones, spheres and cylinders are not polyhedrons.

Common Polyhedra

Tetrahedron Cube Octahedron Dodecahedron Icosahedron   Platonic Solids
triangular prism square prism pentagonal prism   Prisms
triangular pyramidsquare pyramidpentagonal pyramid   Pyramids

Note: the plural of polyhedron is either polyhedrons or polyhedra

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!


Example: Cube

A cube has:

F + V − E = 6 + 8 − 12 = 2

triangular prism

Example: Triangular Prism

This prism has:

F + V − E = 5 + 6 − 9 = 2

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




A diagonal is a straight line inside a shape that goes from one corner to another (but not an edge).

A polyhedron can have lots of diagonals. Can you think of one without diagonals?