Platonic and Archimedean Solids in the Classroom

Actually creating geometric shapes is a wonderful activity for students.  It is an art to form polyhedra.  They are beautiful in and of themselves and inherently pleasing for humans. It may be their symmetry, or the shape of their faces, but students are often fascinated by them.  This combination of art and math is an elegant entry to a study of polyhedra.

In my study of these figures, I chose to create the Platonic solids of tetrahedron and an octahedron.  When truncated, these shapes become the Archimedean solid of truncated tetrahedron and a truncated octahedron.  As I created the figures from paper “nets”, I realized how important it is for students to create such figures.  This hands on experience helps the student understand the figures more deeply.  As you cut and fold, the number of edges, faces and vertices comes to life.

In presenting this to my students, I would offer them a variety of nets with which to work.  Students would be requested to select the figure of their choice, and a truncated version of that same shape.  The data from each figure would be collected on a class chart, detailing the name of the figure, and the number of edges, faces and vertices on each.  The information would then become the focus of a brain storming session, looking for patterns among the data.

The beauty of the figures would be celebrated by creating a public display.  Hanging the figures using thread or fishing string would help others see the shapes clearly.  Using brightly colored paper or patterned paper would highlight the figures even more.  The display would not only please its audience, but also create pride in the students, and increase their interest in Platonic and Archimedean solids.