Identify the features of Platonic solids

Essential Question:
What is duality and how does it tie into the Platonic solids?

Presentation

Folding Polyhedra
Folding & Polyhedra Create Octahedron

Concepts

1. Platonic Solids:
   • All faces are identical regular polygons
     
     
   • Each vertex has the same number of edges/faces converging on it
     
     

Other Resources

• archimedean solids
• snubbing
• Duals

Activities

1. Explore Platonic Solids
   What do Polyhedras have in common?
   
2. Fill in the following:
   
3. Look for patterns
4. Construct the hexahedron/octahedron duality in SketchUp
   
   1. Construct a cube
   2. Locate the midpoints
   3. Connect the midpoints of each face to create an octahedron
   4. Delete the faces that appear inside the cube