Tuesday, 21 May 2013

What nets can be folded into a cube?
Not all nets of six squares can be folded up into a cube, such as a line of six squares, so is there anyway to know what nets can be folded up into a cube with a few simple rules? I am glad to say yes.

Find any point of the net where three squares meet. From this point draw three lines that goes across two squares but diagonally one. Remember where two squares meet you will have two vertices but the lines can't land on anything above three vertices If you can do this the net can be folded up into a cube.

Why across two and diagonally one?
Any point where three squares meet on the net would be the corner of the cube when folded, going across two squares and diagonally one would be the opposite corner of the cube. When the lines go across every square it shows it has to be able to fold into a cube. The lines do not have to go through every square though so how do we know the reminding square is in the correct position? I will not explain it here but you will find that it has to be in the correct position otherwise you would not be able to link three corners to three other vertices.






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