Session 9, Part A:
Platonic Solids (45 minutes)

In This Part: Building the Solids | Naming the Solids

Platonic solids have the following characteristics:

 • All of the faces are congruent regular polygons. • At each vertex, the same number of regular polygons meet.

In order to do the following problems, you will need Polydrons or other snap-together regular polygons. If you don't have access to them, print this Shapes PDF document as a template for cutting shapes out of stiff paper or poster board.

Problem A1

 a. Connect three triangles together around a vertex. Complete the solid so that each vertex is the same. What do you notice? Were you able to build a solid? b. Repeat the process with four triangles around a vertex, then five, then six, and so on. What do you notice?

Problem A2

 a. Connect three squares together around a vertex. Complete the solid so that each vertex is the same. What do you notice? Were you able to build a solid? b. Repeat the process with four squares around a vertex, then five, and so on. What do you notice?

Problem A3

 a. Connect three pentagons together around a vertex. Complete the solid so that each vertex is the same. What do you notice? Were you able to build a solid? b. Repeat the process with four pentagons, then five, and so on. What do you notice?

 Problem A4 Connect three hexagons together around a vertex. Complete the solid so that each vertex is the same. What do you notice? Were you able to build a solid?

 Problem A5 How many Platonic solids are there? Explain why that's the case.

 Session 9: Index | Notes | Solutions | Video