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Edges, Vertices, Surfaces

```Date: 04/22/2003 at 21:37:37
From: Katie
Subject: Edges, vertices, and surfaces

I need help with edges, vertices, and surfaces. How can a shape have
8 edges and 5 vertices? How can a shape have 12 edges, all the same
length? How can a shape have 3 surfaces, one curved?

The one with three surfaces could be a cylinder, but that has 4
surfaces (I think).

Thanks!
```

```
Date: 04/22/2003 at 22:36:44
From: Doctor Peterson
Subject: Re: Edges, vertices, and surfaces

Hi, Katie.

You're right about the cylinder; it is like a soup can, with two flat
ends and one curved "side."

Probably the biggest difficulty here is to try to visualize the shapes
and count their edges. I think these problems all relate to familiar,
ordinary shapes like prisms and pyramids, so if you can find pictures
of those, you can just count the sides. There are pictures of a lot of
shapes in the Dr. Math Geometric Formulas FAQ:

Formulas: Geometric
http://mathforum.org/dr.math/faq/formulas/

Then you need an orderly way to count everything. Let's take a simple
example, the cube:

+------+
/      /|
/      / |
+------+  |
|      |  +
|      | /
|      |/
+------+

You can't see all the edges and surfaces, but you can still think
about them. First, think about the surfaces. We can group them into
top, bottom, and sides: there is 1 top, 1 bottom, and 4 sides, making
a total of 6 surfaces. Now, how about the edges? There are 4 on the
top, 4 on the bottom, and 4 standing upright between the sides,
making a total of 12 edges. Hmmm ... they are all the same length,
too, so you might have an answer here.

Try doing this for other basic shapes, and see if you find one that
fits the other question. You might be able to see a pattern that lets
you find the number of parts of any prism or pyramid when you know
the number of sides in the base.

If you need more help, please write back and show me how far you got.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Polyhedra
Middle School Polyhedra

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