## Good Evening Students,

## It is time to embark on our final task. We are going to attempt to tie together all the material you have learned. It is time to put it all together; you have learned a great amount of knowledge about the five platonic solids. Now let's have some fun. Using your Cabri 3-D technology and your immense knowledge. Create a nested polyhedra that looks similar to the figure to the left. No worries, I will help you step by step. Let the fun begin.

## Sincerely,

## Ms. Barney

## Step One:

Create a cube. This is simple. However, it is important to note the exact side length of your cube. Does your screen look similar to mine?

## Step Two:

What little fact do we know about regular tetrahedrons? Think long and hard about it. Using this knowledge create the figure to the left. See this is not so bad.

## Step Three:

Using the tetrahedron that you have just created, find the midpoints of the edges. These points will now be vertices for your octahedron. Use the convex polyhedron tool to construct your octahedron. Alright, let's move on.

## Are you starting to get the hang of it? If not please refer back to the homepage and e-mail me your concerns.

## Step Four:

Remember that special number we learned earlier in the semester? THE GOLDEN NUMBER. Well, it's back and you will need to you will need to do a measurement transfer of the inverse of the golden number multiplied by your side length of the octahedron to find the vertices of the icoasohedron. Be careful with this step. Make sure all your faces and edges meeth the requirements that assure that you have a regular polyhedron. Once you have all the vertices, use the convex polyhedron tool to construct your icosahedron, and you are almost done. There is only one polyhedron left to nest.

## Step Five:

This is it! You are on the home stretch. The center of each of the icosahedron's faces, are the vertices of the dodecahedron. Use any one of the tehniques we have learned to find the center of the faces. One method is shown to the right. Note in my picture to the right, I have hidden the Cube in the tetrahedron in order to depict the strategy used to contruct the dodecahedron. Once you have found all the vertices there is only one thing left to do. Can you guess what it is? You've got it, use the convex polyhedron tool to construct your dodecahedron.

## You have done it. See it was not that bad. Please save your files and email them to me. In addition, it is important to note the strategies and properties that allowed us to make these constructions. For homework, please do a brief write-up about the knowledge you used to create each solid.