Defining and Counting Faces, Edges, and Vertices of Shapes

Date: 04/06/2004 at 23:34:41
From: LaKesha 
Subject: faces, vertices, edges

How do you find the faces, edges, and vertices of any shape?  I just
go blank, because I really don't understand it.

When I see a question that asks what the faces, edges, and vertices of
a shape are I get really confused and then I stay on that question for
the rest of the time we have to do the test.  I really hope you can
help me!

Date: 04/07/2004 at 12:58:11
From: Doctor Peterson
Subject: Re: faces, vertices, edges

Hi, LaKesha.

You just have to know what the terms mean, and then count them.

A face is a flat surface, like the front or top of a box.

An edge is a line along which two faces come together.

A vertex is a "point" on a shape, a corner where several faces (and 
edges) come together.

They look like this:

        +-----------+
      /           / |
    /           /   |
  +-----------+     |<--- edge
  |           |     |
  |           |     |
  |   face    |     +<-- vertex
  |           |   /
  |           | /
  +-----------+

Now, if you actually have the object in front of you, you can just 
count them all, making sure you count each thing once.  On my box, you 
could count the four vertices on top, then turn it over and count four 
more vertices on the bottom, making a total of 8 vertices.

If you just have a picture, you have to be able to imagine seeing all 
of it, front and back, top and bottom.  And if you just have a 
description (such as "square pyramid"), you have to know what the 
description means, imagine what it looks like, and count in your head.  
That can get a little hard.  But even then, you can count in an 
orderly way, not trying to visualize the details, but just to think 
about different parts of the shape.  For example, a square pyramid has 
a square base, and a triangle going up from each side of the base to 
an apex.  Knowing that, we can do our counting:

  Faces: one square base and four triangles = 5

  Edges: four sides of the base, and four lines to the apex = 8

  Vertices: four corners on the base, and one apex = 5

So by thinking about the parts that go into making the shape, I can 
break down the count into manageable parts without having to see them.

If you have any further questions, feel free to write back.  Let me 
know what kind of problems you are given--do you have pictures?  And 
what kind of mistakes do you tend to make?

Here is some additional help:

  Edges vs. Corners
    http://mathforum.org/library/drmath/view/60418.html 

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 04/07/2004 at 23:30:39
From: LaKesha 
Subject: Thank you (faces, vertices, edges)

Dear Dr. Math,

Thank you so much, this will really help me on my tests!

- LaKesha