Toothpick Tesseract!

A Tesseract is a four-dimensional cube, also known as a hypercube. It's basically the 4D equivalent of our normal 3D cubes, similar to the way cubes are 3D equivalents of squares. Normal tesseracts are usually pictured as a cube within a cube, but for multiple reasons that model is only visually feasible (for example, the sides of the cube inside have to be equal to the bid cube outside, a physical impossibility in our universe).

This is a very simple concept of one way to represent a 4D cube, made out of toothpicks. Of course, you can use anything for the sides, depending how big you want the tesseract to be.

Whether you want to have a really cool bit of math trivia at your house, or just want something interesting as a decoration, this tesseract is yours to make!

You only need a few things to get started making the tesseract:

1) Toothpicks: You'll ideally need 32 to make it, but as a few are bound to get wasted, I'd suggest keeping a stack handy.

2) Cyanoacrylate Adhesive: Its a fancy name for superglue, but make sure that you have it handy. Since toothpicks are thin and weak, this is the only type of glue that can stick them together.

3) A Synthetic, Rubber-based Adhesive: While it's the superglue that will stick the toothpicks together, a rubber-based adhesive will act as the medium for the superglue to act on and effectively stick the delicate toothpicks together.

Optional:

4) A4 Sheets: While not mandatory, I would highly, highly recommend you keep a couple of A4 sheets to do the work on as the glue just spreads everywhere. Look at the sheet above. That's what happened to my sheet.

First off, we have to make a cube. Start by putting two toothpicks together and sticking them with the rubber glue at 90-degree angles.

The next step is applying the superglue. Make sure that you apply the superglue before the rubber-based adhesive dries. This is because the superglue combines with the other glue and makes a very strong matrix which is almost impossible to break.

What you want to do now is make a square with the toothpicks. After that's done, attach a toothpick vertically off the ground. Take care because the toothpick has to be completely straight.

Keep repeating the steps and attaching more toothpicks until the cube is made.

Start making another square. But don't complete the cube! Leave the cube after you've done what's shown in the picture. This is because the the figure has to be fitted into the first cube.

This is a very important step: Align the incomplete cube inside the other as shown in the picture. You'll need to interlock the two cubes. Be very careful while doing this: You don't want to stick the wrong vertices together.

This is going to be tricky to do, but make sure you do it well. Complete the second cube in such a way that the two cubes remain interlocked.

Place the cube upright with one cube upwards and start sticking the corners of the cubes together. In topology, they're called cells.

You might have noticed that when we draw a cube on a flat piece of paper, the 3rd dimension is represented by slants. Similarly, when we try to represent a 4D cube in a 3D model, we represent the 4D edges with slants. Any aliens living in a 4D world will find that the 4th dimension is 90-degree to the others.

After the bottom edges are done, start attaching the top edges. Make sure that that the edges are parallel to each other, as in the first picture.

Now you might have noticed that the rubber glue is forming a spiderweb around the whole tesseract. Don't mind that, because you can take it off very easily at the end.

And that's it! Just leave the tesseract to dry for a few minutes and you're done. It's a cool bit of math trivia, and I hope you really liked it!

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