<This post is a work in progress, with this aside removed once finished penning.>
This post will depict my approach for the Level 4 Menger Sponge construction broken up in two parts: Ability for the bottom cubes to support the overall construction that I'm confident I've solved; The ability for the top four center Level 3 Menger Sponge structures to remain in place sans any outside forces.
The ability for the bottom cubes to support the weight of cubes above it:I propose that the bottom cubes (not necessarily all of them) have inside of them the least amount of business cards rolled into cylinders standing on end. Just enough cylinders to achieve the task at hand so to add the least amount of weight to the overall structure. I constructed one such cube in like matter and it held up tens pounds for days without showing any sign of collapse, hence my confidence.
Proof of concept, as if I had to depict such to you braniacs. (got your attention yet?)
I believe it's very important that the creased folds be as crisp and uniform as possible, thus a machine should perform all the half inch folds at the ends of the business cards, not done by hand.
Part two, with a brief introduction:I've constructed a Level 1 Menger Sponge in 2009
(okay, maybe it was more recently, but that shouldn't matter, right, Marshall Long and Leroy Fodor?)
I went to the local printer here in Sandwich, IL, to purchase his obsolete sheets of color business card stock which he cut into standard 2X3 business cards. After paying for them, I notice that some stock was thicker than others, but still paper oppose to being thin cardboard (cardboard of any thickness is not part of what I envision using). During our conversation after he asked what I was goin' to be using this for, the printer relaid to me how paper has a grain, and that's when it struck me on how to use that truism to construct a Level 4 Menger Sponge. It all boils down to carefully placing the folded cards according to direction of the grain of the paper producing a much stronger build. That, and employing various weights of paper within a certain weight parameter that's predominantly uses for business cards.
The only other difference in the cards is if the paper was specially designed, purposely making it stronger for the six(?) different weights needed for the construct. Now, I'm not talking about metal strands woven inside the paper, or any other substance that would be considered cheating, but a special paper formulated may be need for the structure to hold. Then again, not necessarily, but an option on the table nonetheless.
That said, there's one more trick I have up my sleeve as to how those top four center Level 3 Menger Sponges can be held in place.
First, let's recap:Business card stock comes in different weights which would be used to our advantage: Heavier stock used on the bottom; lighter stock for the construction of cubes at the top. The placement of each card being crucial. Same true as to the weight of the stock used for the cylinders.
Paper has grain, another fact we can use to our advantage. If a business card is standing on edge lengthwise, it would hold more weight if it consist of two-inch vertical grains oppose to three-inch horizontal grains. More so being true if the card is laying flat, especially when used for the construction of the four center Level 3 cubes at the top. The grain must be taken into consideration for the construction of the cylinders to help minimize the number of cards needed for the build.
Now, for the trick I have up my sleeve which adds more weight, but hopefully it's desired affect offsets that while making those four crucial top cubes stronger and maintains its rigidness.
One more thing before I get into that. Temperature and humidity should be highly consider during and after the build since we're talking about paper. One can easily imagine what would happen to even the best paper structure built if the humidity were too high over a period of time. Perhaps, keeping the temp at a constant 70
o would help maintain its integrity, always being mindful of body heat let off from those visiting the structure unless it's fully enclosed.
Actually, there's two tricks I've devised to hold the top four center sponges rigid. One, is to incorporate double flaps on the leading edge of each cube at both ends of the Level 3 sponge that's attached to the columns. The other is sliding an unfolded card on each side of the cubes that, again, are at the leading edge, all the while being mindful of the cards' grain direction. It's this aspect that needs scrutinized since Level 3 sponges weigh ~150 lbs each, thus 512 connection points will be holding ~75 lbs between them.
The decorative cladding would be of cards of lighter weight unless placed strategically for structure integrity. Same true for the makeup of cubes not having cubes directly above them.
The cladding cards could depict an image of a major sponsor, or once finished all the cladding combined depicts a large image representing some sponsor.
Poll
