Construct a Cube

The object of this puzzle is to reconstruct a cube from ten tetrahedral pieces. You can make the ten tetrahedral puzzle pieces by printing this page, and cutting out the shapes shown below. Tape the edges of each piece together to make a tetrahedra.

Remember to make four copies of the first piece. (This is also hint about how to do one of the decompositions).

• Piece one (make 4):
  
• Piece two:
  
• Piece three:
  
• Piece four:
  
• Piece five:
  
• Piece six:
  
• Piece seven:
  

How many different ways of assembling a cube out of these pieces can you find? You should find at least 3 different decompositions before you give up, and look at the answer.