How to cut a cube into an icosahedron? Edit: Originally I asked this about a using a cube, but it is not a requirement to start with a cube, just how to end up with an icosahedron as on of the answers showed how to make dodecahedron a having started ith any shape.
I have a cube, and I need to cut/file it into a icosahedron; what are the cut lines?
Same question for other Platonic solids: is it easy to start with a cube and get other shapes, Or is it better to choose a different solid as a starting point? I am asking this question from a physical/practical point; otherwise one can very well start with sphere (it is hard to file/cut a piece of wood/metal into a sphere).


Six of the thirty icosahedron edges and all twelve of its vertices lie on faces of the cube. Each icosahedron vertex lies near one cube edge and there is clearly the same number of icosahedron vertices as cube edges. $\dots$
  Finally, from the model, observe that it is easy to list the $(x,y,z)$ coordinates of the twelve vertices:
  
  
*
  
*$(\pm 1 , \pm \phi, 0)$,
  
*$(0, \pm 1, \pm \phi)$, and
  
*$(\pm \phi, 0, \pm 1)$, where $\phi$ is the golden ratio.
  

from here.
