Polyhedron
A polyhedron is a solid with flat faces (from Greek poly meaning "many" and edron meaning "face").
Each flat surface (or "face") is a polygon.
So, to be a polyhedron there should be no curved surfaces.
Examples of Polyhedra:
Triangular Prism  Cube  Dodecahedron 

Common Polyhedra
Platonic Solids  
Prisms  
Pyramids 
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 the "Polyhedral Formula", and is very useful to make sure you have counted correctly!
Let's try some examples:
This cube has:
 
F + V  E = 6+812 = 2 
This prism has:

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