Polyhedra V1.0

• The 5 polyhedra
  
  
• Tetrahedron
  
  • +Tetrahedron
    
  • +Octahedron
    
  
  
• Cube
  
  • +Tetrahedron
    
  • +Octahedron
    
  • +Icosahedron
    
  
  
• Octahedron
  
  • +Tetrahedron
    
  • +Cube
    
  • +Icosahedron
    
  
  
• Dodecahedron
  
  • +Tetrahedron
    
  • +Cube
    
  • +Octahedron
    
  • +Icosahedron
    
  
  
• Icosahedron
  
  • +Tetrahedron
    
  • +Cube
    
  • +Dodecahedron
    
  
  

Octahedron

(The image is an applet: you can click and drag it).

The midpoints of 6 dodecahedron edges are the vertices of the octahedron.