Menger Sponge Business Card Shenanigans


What can I do with my old business cards? That’s what I asked myself when one of the companies that I work for moved offices. Yup, you heard that right, I’ve actually got a job. Hard to imagine, I know. Well, building a Menger sponge is some sick trick that you can pull out of the bag.


source: IFF

No. we’re not talking about the Arsenal manager, that’ll be Arsene Wenger, or those crazy Dutch Eurodance nutters banging on about going to Ibiza. That’ll be the Vengaboys.


source: Vengaboys (yes, I’m afraid this actually happened)

No, today we’re talking about the Menger sponge and how you can make one yourself with a bunch of old business cards.

Not got any business cards? Nick a load off your dad or your pals who have actually got a job. Your paper round doesn’t qualify as a job that you need business cards for.

You’ll need a lot of business cards though. Maybe get some printed from one of those machines in a motorway service station. And while you’re at it you may as well form a company.


When I was 18, me and a buddy took a road trip to Ferry Bridge services, got some cards made up and BOOM, Assassin Autos was born. Our strapline? We kill the opposition. Aaah yeah. We were proper knobheads.

Anyways, the Menger sponge is a type of fractal. A fractal is something that has a repeating pattern at every level of scale. It’s seen in snowflakes and can also be used to define the creation of galaxies. Dang, these fractals can be found everywhere, here are just a few things that are made up of fractals:

  • River networks
  • Fault lines
  • Mountain ranges
  • Craters
  • Lightning bolts
  • The horns of a mountain goat
  • Trees
  • Pineapples
  • Your own heart rate, dude
  • Earthquakes
  • Crystals
  • Your blood vessels
  • Ocean waves
  • DNA
  • Proteins

Repeating patterns are everywhere.

So, this boffin dude, Karl Menger, came up with the idea of a fractal solid that’s just one big cube. Picture that in your tiny mind, yeah?

Now remove the cube in the center of each face and the cube right in the center of the cube. So, you’re left with a structure consisting of the eight small corner cubes plus twelve small edge cubes holding them together.

Still with me?

Now, keep repeating this process on each of these remaining 20 cubes. Repeat again. And again. Forever.


source: Wikimedia

You’ll either get proper bored or have a really cool Menger sponge. Cheers Menger dude, you da bomb.

Another way of doing it is to build it all up from the individual cubes. That’s where the business cards come in.

So, get them business cards out, place them down on the table and let’s go whoopass on the whole Menger business card scenario.

First, grab two cards and place them on top of each other at right angles. Centre them as much as possible and fold the flaps over on each card.


You’re going to need to do six cards like that for your first cube.

Pull the two cards apart and start the assembly. Six of them can be put together as shown below to make a cube. All flaps must be on the outside of the finished cube, you string bean rip-chain looking fool.



Two cubes can be linked together by taking  the two flaps on one face and tucking them under the corners of the two flaps on the adjacent face of the other cube. This is pretty dang solid.


Keep adding cubes like this to build up your Menger sponge.


Have fun, buddy, and keep on going. It’d be great for me to see how you’re getting on. Let me know how your business card baby keeps on growing. Get in touch and tell me all about it.

You is a lightning bolt, an earthquake. Oh, and also a pineapple. Your ninja skills are fully activated.

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