The exercises contained in this activity require the *KaleidoTile*
program developed by Jeff Weeks. If you do not yet have a copy of this
software, you may wish to
download *KaleidoTile*
.

For more information regarding this activity and its objectives, see the accompanying Teacher's Guide.

1. Get models of the five Platonic solids to study. Each Greek prefix in the table below represents a number. Name each Platonic solid shown in the lower table by:

- counting the number of faces,

- find the Greek prefix that matches the number of faces,

- attach this prefix to "hedron".

- For example, a polyhedron with 5 faces could be called
*pentahedron*.**Table: Greek Prefixes**Prefix Number Prefix Number mono 1 hendeca 11 di 2 dodeca 12 tri 3 trideca 13 tetra 4 tetradeca 14 penta 5 pentadeca 15 hexa 6 hexadeca 16 hepta 7 heptadeca 17 octa 8 octadeca 18 ennea 9 enneadeca 19 deca 10 icosa 20**Table: Names of the Platonic Solids**Platonic Solid Number of Sides Name

If so, explain why.

3. Load the

- In the
**Basepoint**window, drag the base point to each vertex dot and write the name of the polyhedron formed in the (2,3,4) -Family Diagram.

- Starting with the base point at the lower right vertex dot, slowly
drag the base point along the right edge of the base triangle triangle
until you reach the dot in the middle of the edge. Watch as the cube
transforms into a new polyhedron. Describe how the polyhedra are
changing.
- Continue to drag the base point along the right edge of the base
triangle until you reach the upper vertex dot. Again describe how the
polyhedra are changing.
- Place your base point at the lower left vertex dot. Slowly drag the
base point along the left edge of the base. Describe what happened to the
Platonic solid as you moved the base point away.
- Give your own definition of the word
*truncated*. - Notice that the name of the polyhedron at the top vertex dot is a
combination of the names of the two Platonic solids in lower vertices.
Why do you think that is?
- Starting at the top vertex, slowly drag the base point straight down
toward the dot in the center of the triangle. You are
*truncating*the polyhedron. Pause when you reach the center dot. Then continue until you reach the dot in the middle of the lower edge. Note that these last two polyhedra names have*rhombi*in them. What do you think*rhombi*means?

4. It's time to check what you learned by studying a different family of polyhedra, the (2,3,5)-family. Change the

- Fill out the (2,3,5)-Family Diagram below by dragging the base point
to each vertex dot.

- Once again, starting with the base point at the lower right vertex
dot, slowly drag the base point along the right edge of the base triangle
triangle. Similarly, start at the lower left vertex dot and drag the
base point along the left edge. What word describes what is happening in
both cases?
- Starting at the top vertex, slowly drag the base point straight down
toward the dot in the center of the triangle. Pause when you reach the
center dot. Then continue until you reach the dot in the middle of the
lower edge. What shapes do these last two polyhedra have that give them
*rhombi*in their name? - Explain what
*rhombitruncated icosadodecahedron*means.

5. Let's see if you know what is really going on.

- Two names of the (2,3,3)-family are given in the diagram below.
Use what you learned from studying the (2,3,4)- and (2,3,5)-families to
fill in the other five names. Do NOT use
*KaleidoTile*for this! It will give you incorrect names.

*KaleidoTile*gives some different names than you should have written. Change the**Symmetry Group**by pressing the**(2,3,3)**button. Fill out the (2,3,3)-Family Diagram below, this time using*KaleidoTile*.

- Explain why
*KaleidoTile*named these polyhedra differently than it did for the first two families.

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