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### Geometry and Soccer balls

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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?

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/
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Associated Topics:
High School Geometry
High School Polyhedra
Middle School Geometry
Middle School Polyhedra

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