Challenge

Build Platonic Solids

Oil painting of Johann Neudörfer earnestly showing Platonic solid models to a slightly distracted student circa 1590
Johann Neudörfer working with a student possibly his son Johann the Younger circa 1561. © Germanisches Nationalmuseum

Build regular convex polyhedra with only one type of regular polygon.

  • How many Platonic Solids are there? What are they called? Can you prove there are no more?
  • What does face-transitive mean? In what ways are the shapes symmetrical?
  • What is the history and significance of the Platonic Solids? What did they represent to Plato?
  • How can you extend or transform these shapes to create new ones? What is Albrecht Dürer's solid? What does it mean?
  • How can you display an arrangement of the platonic solids together?
  • What are the shadows cast by these shapes like when projected on different surfaces from different light sources? What is a Petrie polygon?

For answers, notes, and supporting materials, enter your license code.

Enter Premium License

Pinned images from our dedicated Pinterest board.