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
    
  
  

Icosahedron

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

On the 6 faces of the cube draw 6 segments parallel to the cube edges. The ratio between the length of the segments and the length of the cube edge must be the golden ratio (1.6180339887498948482...). The 12 ends of the segments are the vertices of the icosahedron.
One of my favorite inclusions!