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# "256"

• G2086
• F106
• D15
• 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!:)