Geometry and Soccer balls

Date: 10/29/98 at 10:50:00
From: Megan Monaghan
Subject: Geometry/Soccer balls

Hi,
We are studying geometry right now. I am supposed to make a math 
project or display for our bulletin board. Since I love soccer, I would 
like to do something fun about the shapes on a soccer ball. Do you have 
any ideas?

Thank you for your help,
Megan Monaghan

Date: 10/29/98 at 15:57:48
From: Doctor Tom
Subject: Re: Geometry/Soccer balls

Here are a couple of ideas. First, look carefully at a soccer ball and 
you'll see that it's the intersection of two Platonic solids - the 
icosahedron and the dodecahedron. In fact, like the dodecahedron it has 
12 5-sided faces, and like the icosahedron it has 20 6-sided faces.

You might look at Euler's formula, which relates the number of faces, 
edges, and vertices of a solid. For example, a cube has 6 faces, 12 
edges, and 8 vertices (corners). The tetrahedron has 4 faces, 6 edges, 
and 4 vertices.

If you take ANY solid without holes that's made of flat faces like 
this, and F = number of faces, E = number of edges, and V = number of 
vertices:

   F - E + V = 2

For the cube:          6 - 12 + 8 = 2  
For the tetrahedron:    4 - 6 + 4 = 2 

Find the numbers for some other shapes, and for your big example, do 
the soccer ball.

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