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

You are watching: All polyhedrons are prisms or pyramids

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

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

Common Polyhedra

 Platonic Solids Prisms Pyramids

Note: the plural of polyhedron is one of two people polyhedrons or polyhedra

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 Explore 100s of animated Polyhedron Models.You can likewise see some photos of Polyhedra if girlfriend want.

Counting Faces, Vertices and also Edges

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

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

This can be written nicely as a small equation:

F + V − E = 2

It is known as Euler"s Formula (or the "Polyhedral Formula") and also is really useful come make sure we have actually 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 cases where it does not work! check out Euler"s Formula because that more.

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Diagonals

A diagonal is a straight line within a form that goes native one edge to one more (but not an edge).

A polyhedron deserve to have several diagonals. Have the right to you think that one there is no diagonals?

Geometry solid Geometry Platonic Solids prisms