The two platonic solids I started out with were a cube and a tetrahedron.
As a result of truncating the cube, there were 8 equilateral triangles and 6 regular octagons. 14 Faces + 24 Vertices – 2 = 36 Edges
As a result of truncating the tetrahedron, there were 4 equilateral triangles and 4 regular hexagons. 8 Faces + 12 Vertices – 2 = 18 Edges
I think my students would enjoy creating the Archimedean Solids; anything that’s hands-on is usually enjoyable. Truncating the solids, on the other hand, would be a bit more challenging, for some. Since both grade levels would have prior knowledge of 2-D & 3-D figures, I would definitely have them create all of the Archimedean Solids, so they could analyze the characteristics of each. Additionally, I would have them truncate the cube, only, so they can describe the transformation and make predictions about the faces, edges and vertices. Since many of my students are avid soccer fans, I would use the dodecahedron as a model during my anticipatory set, and display all of the solids on the bulletin board, after the lesson is completed.
Teachers Rule With Class 
Jul 19, 2012 @ 12:34:48
I am really impressed by how “neat” your archimedean solids turned out. My final product ended up a little less polished. I think the next time I do this activity, I will try using thicker, construction paper. I also love how you tied in the idea of a soccer ball. Students can definitely relate this concept to something they use everyday.
Jul 20, 2012 @ 18:09:03
I agree that some students may have difficulty truncating the solids. It looks as though you have done this before! Relating the dodecahedron to soccer will peak student interest. I’m sure they will love to see their soccer balls on the bulletin board!
Jul 20, 2012 @ 18:10:25
Oh my goodness your figures are perfect! How did you do that?! Mine are a disaster! I better perfect this skill before I ever teach it! Great job! I like how you mentioned having students just truncate the cube to understand the concept.