Mega Menger: Building a Menger Sponge at MIT

MIT’s origami club, OrigaMIT, led the effort to build a Level 3 Menger Sponge out of folded business cards. This was part of a larger, global project sponsored by Queen Mary University of London.

A Menger Sponge is a three-dimensional fractal, which can be made by taking a cube and cutting out a square section through the center in each of the three directions; then each of the resulting smaller cubes is cut out in the same way, and so on until you’ve removed infinitely many pieces. The Mega Menger Project aimed to construct the largest Menger Sponge ever built using only business cards.


Suppose you take a cube and cut it up into 27 smaller cubes. And then, after that, you take out every cube on the face of the original cube. And then the cube in the middle of the original cube, you end up with 20 cubes left that kind of like form like a frame of the original cube, that’s a level one venture lunch.

And then, to make a level two major sponge, you repeat the process on every one of the 20 constituent cubes you made from cutting up your original cube. So if you keep going, you eventually make a three-dimensional fractal curve with zero volume and infinite surface area.

So that’s a major sponge. Our mentor sponge was part of a larger project called the mega Menger, sponsored by the Queen Mary University of London. And the idea was that 20 sites around the world would each build a level three major sponge. So that, in theory, we would have together make a level four major sponge. And that’s the largest mental sponge that’s ever been built out of business cards.

So when we decided that we wanted to full this love and built this sculpture, we thought that this was a great way to do it within our club and get the entire MIT community involved. We held club meetings, and we had regular breaks. And we got many people, from first-year students to seniors, graduate students to faculty and staff, coming and folding this thing with us.

The cool thing is that manga sponge has an unexpected connection to MIT. Because one of the first, if not the first, people to build this structure out of this discards was Dr. Janine Mosley, who did her Ph.D. at MIT. And she’s currently this tremendously successful and prolific origami artist
Almost 20 years ago, I learned how to make the business card cube from some verbal instructions.

Initially, I wasn’t particularly excited about the cube because it’s not, you know, that exciting shape. But after a while, my son taught him to make the cubes, and he was playing with them. And I had two cubes that were exceeded, side by side on a table, and I was looking at his cubes, and I said, Oh, my God, look at the flaps, you can tuck them under each other like this. And if you do, you’ll end up with two linked cubes. And they’re very firmly attached. And you can add more and more cubes and build on any structure you can think of.

Around this time, the company that I was working for changed its name. And all my co-workers who knew that I’d been doing origami with business cards came by and gave me their old business cards. And so I had a very, very large collection of business cards to work with. And, and I was someone’s teasing me, what are you going to build with all those cards, and I said, Oh, I don’t know, maybe I’ll build a level three approximation to a Menger sponge. I only need 48,000 cards to do that. It took me ten years. And I finished it in 2005. And since then, many people who’ve read about it have said, Hey, I want to build one too. But what we didn’t realize was how much work and building a level three major sponge would be.

Once we started folding, we’re like, oh, this is kind of the this will be super time-consuming. And we paid off more than we can chew. So instead of building the whole level three-month mango squad, we just made one of the rings that form one of the faces, which would be eight-level twos. And this would be only 25,000 business cards.

We also heard recently from the worldwide mega project that including us, when you combine everybody’s built together, build a level four. And that’s insane in terms of the number of business cards, the number of person-hours. I think to be part of that was super excited.

By the manga response, I don’t know there’s something about it that just everybody seems captivated by it. And it’s important, and I guess that when you set out to build something big, and you want to get hundreds of people to help, the end goal needs to be something that inspires them and makes them want to persevere and keep going until it’s done.

Ali Kaya


Ali Kaya

This is Ali. Bespectacled and mustachioed father, math blogger, and soccer player. I also do consult for global math and science startups.

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