Session 9: Solids

Session 9, Part A:
Platonic Solids

In This Part: Building the Solids | Naming the Solids

When working with three-dimensional figures, the terminology can get confusing. (What would you call a side?) It helps if everyone uses the standard names:

The Platonic solids are named for the number of faces they have.

Problem A6

For each of the Platonic solids, count the number of vertices, faces, and edges. This is harder than it sounds! Think about how to "count them without counting them."

Counting vertices and edges can be tricky. Think about how to "count without counting." How many faces are there on the polyhedron? How many vertices on each face? How many faces meet at a vertex on the polyhedron? You can put all of this information together to "count" the number of vertices. Close Tip


Problem A7
Find a pattern in your table. Express it as a formula relating vertices (v), faces (f), and edges (e).


Problem A8
Does your pattern hold for solids other than the Platonic solids? Build several other solids. Count the vertices, faces, and edges, and find out!

Video Segment
In this video segment, the participants build solids and start to make conjectures about the relationship between angles, edges, and faces needed to build them. Watch this segment after you've completed Problems A6-A8.

How many solids were you able to build? Were you convinced that there are only five Platonic solids?

If you are using a VCR, you can find this segment on the session video approximately 5 minutes and 40 seconds after the Annenberg Media logo.

Next > Part B: Nets

Session 9: Index | Notes | Solutions | Video