Nets of Dice - how to know if it is a Nets of Dice












1














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 -
enter image description here



And some examples for clarity - these figures can be net of dice and may be not:



enter image description here



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?






geometry discrete-mathematics education dice







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  • I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
    – Ethan Bolker
    Nov 22 '18 at 1:43












  • Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
    – Programmer
    Nov 22 '18 at 1:52
















1














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 -
enter image description here



And some examples for clarity - these figures can be net of dice and may be not:



enter image description here



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?






geometry discrete-mathematics education dice







share|cite|improve this question
























  • I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
    – Ethan Bolker
    Nov 22 '18 at 1:43












  • Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
    – Programmer
    Nov 22 '18 at 1:52














1












1








1







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 -
enter image description here



And some examples for clarity - these figures can be net of dice and may be not:



enter image description here



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?






geometry discrete-mathematics education dice







share|cite|improve this question















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 -
enter image description here



And some examples for clarity - these figures can be net of dice and may be not:



enter image description here



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?






geometry discrete-mathematics education dice




geometry discrete-mathematics education dice






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 22 '18 at 1:56

























asked Nov 22 '18 at 1:36









Programmer

2073413




2073413












  • I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
    – Ethan Bolker
    Nov 22 '18 at 1:43












  • Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
    – Programmer
    Nov 22 '18 at 1:52


















  • I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
    – Ethan Bolker
    Nov 22 '18 at 1:43












  • Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
    – Programmer
    Nov 22 '18 at 1:52
















I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
– Ethan Bolker
Nov 22 '18 at 1:43






I'm not sure what you are asking. Any net of six squares that will fold into a cube can be numbered to make a legal die. (Note that the "opposite faces sum to $7$" allows for two possible solutions, one the mirror image of the other. All dice legal in casinos are of the same kind. Occasionally you'll find both kinds at an elementary school.)
– Ethan Bolker
Nov 22 '18 at 1:43














Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
– Programmer
Nov 22 '18 at 1:52




Thanks - my question is we need to fill in the numbers in the figures to ensure that the net can form a dice as in example . I am not sure which face will be opposite to other and where what number to fill from 1-6
– Programmer
Nov 22 '18 at 1:52










1 Answer
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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.






share|cite|improve this answer





















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    1 Answer
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    1 Answer
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    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.






    share|cite|improve this answer


























      0














      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.






      share|cite|improve this answer
























        0












        0








        0






        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 22 '18 at 1:58









        Ethan Bolker

        41.8k547110




        41.8k547110






























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