A polyhedron is a hard with level faces(from Greek poly- meaning "many" and -hedron definition "face").

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CubeIts deals with are all squares
Triangular PrismIts deals with are trianglesand rectangles
DodecahedronWhat encounters does that have?

So no bent surfaces: cones, spheres and also cylinders room not polyhedrons.

Common Polyhedra

Platonic Solids

Note: the many of polyhedron is either polyhedrons or polyhedra

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Explore 100s of animated Polyhedron Models.

You can also see some photos of Polyhedra if girlfriend want.

Counting Faces, Vertices and also Edges

When us count the number of faces (the level surfaces), vertices (corner points), and edges the a polyhedron we find an amazing thing:

The variety of facesplus the number of verticesminus the variety of edges amounts to 2

This deserve to be written nicely as a little equation:

F + V − E = 2

It is known as Euler"s Formula (or the "Polyhedral Formula") and also is really useful to make certain we have counted correctly!

Example: Cube

A cube has:

6 Faces8 Vertices (corner points)12 Edges

F + V − E = 6 + 8 − 12 = 2

Example: triangular Prism

This prism has:

5 Faces6 Vertices (corner points)9 Edges

F + V − E = 5 + 6 − 9 = 2

But over there are instances where the does not work! check out Euler"s Formula for more.

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A diagonal is a right line inside a shape that goes native one corner to an additional (but not an edge).

A polyhedron deserve to have lots of diagonals. Can you think the one there is no diagonals?

Geometry solid Geometry Platonic Solids prism