Kunkus
"Platinum" - 18 Interlocking Rectangular Prisms #3
"Platinum" - 18 Interlocking Rectangular Prisms #3
Designed and folded by me out of copy paper.
Prism Theory: This design, like Osmium, follows a pyramid split layering pattern. I then actually played around with the permutations on POV-ray and eventually chose this design because of its beautiful 3-fold axis.
If you define each type of prism based on coordinates from the origin, most permutations of lengths will yield valid compositions as long as every length is unique. I make mine linearly scaled so these compositions will have maximum density which is why I am naming them after dense metals. You can swap essentially any two lengths at any time or assign lengths in many different patterns for different effects.
The number of total possible compositions depends on the layering scheme, but for this layering scheme that uses 12 lengths, the upper bound for possible viable compositions is 12!. Most of these won't necessarily be aesthetic cause they won't follow nice patterns. Some permutations won't yield valid compositions simply because you won't have interlocking prisms or because prisms will intersect on a triple split if you make the middle prisms coordinate on the split axis larger than the coordinates for the other two prisms on the split axis. There will probably be around 10! to 11! permutations that yield viable compositions with many of these being duplicates. I'm not going to try and calculate the exact amount but there are so many to be explored.
"Platinum" - 18 Interlocking Rectangular Prisms #3
"Platinum" - 18 Interlocking Rectangular Prisms #3
Designed and folded by me out of copy paper.
Prism Theory: This design, like Osmium, follows a pyramid split layering pattern. I then actually played around with the permutations on POV-ray and eventually chose this design because of its beautiful 3-fold axis.
If you define each type of prism based on coordinates from the origin, most permutations of lengths will yield valid compositions as long as every length is unique. I make mine linearly scaled so these compositions will have maximum density which is why I am naming them after dense metals. You can swap essentially any two lengths at any time or assign lengths in many different patterns for different effects.
The number of total possible compositions depends on the layering scheme, but for this layering scheme that uses 12 lengths, the upper bound for possible viable compositions is 12!. Most of these won't necessarily be aesthetic cause they won't follow nice patterns. Some permutations won't yield valid compositions simply because you won't have interlocking prisms or because prisms will intersect on a triple split if you make the middle prisms coordinate on the split axis larger than the coordinates for the other two prisms on the split axis. There will probably be around 10! to 11! permutations that yield viable compositions with many of these being duplicates. I'm not going to try and calculate the exact amount but there are so many to be explored.