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:


F + V − E = 6 + 8 − 12 = 2 
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.
Note: the plural of polyhedron is either polyhedrons or polyhedra