Matematika Ria
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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

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