# How to Build Level-One Menger Sponge?

In this project, we are going to build a level one Menger sponge. To make a level one Menger sponge, we’ll need 20 of these to make a level two sponge.

These are the cards we’ll be using to build the Menger sponge.

Ingredients:

STEP 1

First, you’ll need to fold the cards. An easy way to make sure they’re at right angles is to place two at right angles. When you fold over both sides, you will see that the folds will be perpendicular.

STEP 2

Now, you need to fold the top and bottom sides of the middle card. But before that, you should slide the middle card so that there is an equal amount of top and bottom.

STEP 3

Separate the cards. You will have two square cards, and on the back of each will be two tabs to join the cards together.

STEP 4

Since a cube has six faces, we need six folded cards to get our cards into a cube. Make sure that the tabs will always remain on the outside of the finished cube. It would help if you also remembered that you’ll always put an edge with a tab against an edge without a tab whenever you put two cards together.

STEP 5

The best way to assemble the cards is to start placing one card down on the table and putting one vertical card under each side.

STEP 6

You can then add a fourth card horizontally on one side, and a fifth card can then go opposite the fourth card horizontally. Make sure that all of the tabs are still on the outside of the cube.

Finally, you get the basic unit of construction of the Menger sponge.

STEP 7

To join together two cubes, you need to use the tabs. Remember the tabs on each cube either run horizontally or vertically on each face. To put two together, you’ll need horizontal tabs on one and vertical tabs on the other to lock together the corners of the tabs. Then we get two cubes are attached.

STEP 8

To cover your Menger sponge, you can use the provided design cards that show levels of a fractal. You can download them here print your own.

STEP 9

You need to fold the tabs of the provided design cards like the blank card. You can use the lines to work out where the folds will be. Then you will get squares that have tabs on the back to attach them to the cubes.

STEP 10

Place the designs at right angles and tuck all four corners underneath. The outside layer not only makes it look nice but also makes it structurally stronger. We should also use the outside covering cards at this stage to fill the gaps in between the cubes. It won’t be easy to get into once we finish building our level one sponge.

STEP 11

To have a level two Menger sponge, we need 20 level-one Menger sponges, making 400 cubes.

### 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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