I am school student and learning Visualizing Solid Shapes. In this chapter we have a concept that if piece of paper is cut in a net shape we need to prove that the same can be formed into a dice (opposite side sum should be 7).
I am a little confused on same - below are the some shapes -
And some examples for clarity - these figures can be net of dice and may be not:
The issue is that given an empty net how can I know if it can be used to make dice. We need to fill in the numbers from 1-6 and if all opposite faces sum of numbers comes to 7 then it is a dice - as in example . I am not sure that given an empty net which face will be opposite to other and where what number to fill from 1-6 - I mean I am not able to conclude of different shapes of net which face will be opposite to which face - hence cannot write proper values of number in each face?
Is there an way that we can find or understand the same?
Here's a strategy. Put a $1$ in some square. Then cross over each edge of that square to the four neighboring squares - you may have to imagine the folding to do that. The square you haven't reached is the one to mark $6$. And so on with the other two pairs.
I don't know whether this counts as a solution for you. It's not an automatic procedure, but it is guaranteed to produce one of the two legal numberings.