# Regular solids

For each of the 5 regular polyhedra, enumerate the number of vertices (v), edges (e), and faces (f), and then evaluate the quantity v - e + f. (One of the most interesting theorems relating to any convex polyhedron is that v - e + f = 2. -> This was given as part of the problem. I am not sure if it is of any value when solving this problem or not.)

Please use pictures to illustrate the concept above along with a detailed explanation of your response. Thank you.

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#### Solution Preview

See attachment please!

A polyhedron is a 3-dimensional closed figure made from flat sides, or 'faces'. There are an infinite number of them. A barn, for example, has many flat surfaces or faces; it's a polyhedron. So it a textbook. A prism. The diamond in a ring. All these figures are made from flat 'faces'.

But on each one of the objects mentioned above , some of the faces are different shapes. Is there a polyhedron with all the faces the same?

Yes there is. In fact, there are just five of them! You are familiar with at least one of them ...

#### Solution Summary

This shows how to find the number of vertices (v), edges (e), and faces (f) of polyhedra.