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
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:
- 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 |
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