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"256"

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How to create many of regular, crazy and impossible object using only 4 modules
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  • 256
    di De Nigris Daniele
    How to create many of regular, crazy and impossible object using only 4 modules. I'm not a mathematician,
    so I hope that all arguments are correct. I do not know if these objects were already created, but it was very interesting to create them. However this project will be useful in the future. I hope that this topic interests you. Have a good vision. For any clarification: denigrisdaniel@gmail.com
  • Create a grid of 15x15 squares
  • Create this parallelepiped following the grid
  • Apply two orthogonal lines passing through the center of the figure
  • Now the figure is composed of 4 different modules
  • The 4 modules
  • In this scheme you can see that each module has the same attachment point. All modules can be joined together
  • Some examples of possible combinations
  • That is the question
  • "256" this is the number of the possible combinations (O.M.G.They are too numerous)
    When I start to create all the combinations I realize that some are the same (the only difference that they are rotated). So, I decided to study this scheme, to try to eliminate the possibility that repeat themselves.
  • The 256 combinations are composed of 7 groups:
    A: 4 squares with same color
    B: 3 squares of the same color + 1 square with a different color
    C: 2 squares on the same side with the same color + 2 squares on the same side with the same color
    D: 2 squares on the diagonal with the same color + 2 squares on the diagonal with the same color
    E: 2 squares on the same side with the same color + 2 squares on the same side with the different color
    F: 2 squares on the diagonal with the same color + 2 squares on the diagonal with the different color
    G: 4 squares with different color
  • Group A: There are 4 combinations
  • All 4 combinations are different
  • Group B: There are 48 combinations

  • There are only 12 different combinations. The remaining 36 combinations are the same (they are only rotated)
  • Group C: There are 24 combinations
  • There are only 6 different combinations. The remaining 18 combinations are the same (they are only rotated)
  • Group D: There are 12 combinations
  • There are only 6 different combinations. The remaining 6 combinations are the same (they are only rotated)
  • Group E: There are 96 combinations
  • There are only 24 different combinations. The remaining 72 combinations are the same (they are only rotated)
  • Group F: There are 48 combinations
  • There are only 12 different combinations. The remaining 36 combinations are the same (they are only rotated)
  • Group G: There are 24 combinations
  • There are only 6 different combinations. The remaining 18 combinations are the same (they are only rotated)
  • That is the second question
  • "70" this is the number of the different possible combinations
    But now I found another problem: when I start to create this 70 combinations I realize that some combination are specular. So, I decided to study this problem, to try to eliminate the possibility that repeat themselves.
  • I understand the problem: the red module and the gray module, are specular. So I decide, to reflect all the 70 combinations, to find any similar combinations.
  • There are only 3 different combinations. The remaining 1 combination is the same (It's specular)
  • There are only 7 different combinations. The remaining 5 combinations are the same (they are specular)
  • There are only 4 different combinations. The remaining 2 combinations are the same (they are specular)
  • There are only 4 different combinations. The remaining 2 combinations are the same (they are specular)
  • There are only 14 different combinations. The remaining 10 combinations are the same (they are specular)
  • There are only 7 different combinations. The remaining 5 combinations are the same (they are specular)
  • There are only 4 different combinations. The remaining 2 combinations are the same (they are specular)
  • That is the last question
  • "43" this is the number of the different possible combinations.
    From 256 to 43 ...sounds good!
  • ...finally
  • Take a random combination
  • We create two areas:
    The colored areas: they tell us how to color the picture.
    The white areas: for each combination, they will have a different color.
  • Take the right colors to the "colored areas"
  • after applying the color to the "Colored areas" we can apply the color the
    "white areas"
  • Remove the excess filets and replace the color combination with the letters.
    Now we can created all the 43 combinations.
  • combinations 1-4
  • combinations 5-8
  • combinations 9-12
  • combinations 13-16
  • combinations 17-20
  • combinations 21-24
  • combinations 25-28
  • combinations 29-32
  • combinations 33-36
  • combinations 37-40
  • combinations 41-43
  • One example with a best rendering
  • One example with a best rendering
  • THANK YOU FOR WATCHING!:)

    ME ON FACEBOOK

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