How to Draw a Tesseract

Reviewed by Jeanine Hattas Wilson

Last Updated: July 1, 2021

A tesseract is a four-dimensional shape. It is the four-dimensional analog of a cube. It is possible to draw a cube on a flat surface by distorting the angles and lengths in a way that our minds perceive depth. It is also possible to draw extra-dimensional shapes (like tesseracts) in this way.

Steps

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1
Gather your supplies. You will need paper and something to write with. A pencil is preferred if you want to erase things, but any writing utensil will do.
2
Draw a square roughly in the center of the page. Putting it down and to the left or right might make the rest of the drawing easier. It doesn't have to be perfect. Not even computer generated squares are.

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3
Add a square linking with the first. It should start halfway across the top of the first and intersect again halfway down. Ideally, these would be congruent, but they don't have to be.
4
Notice that a third square is made by linking these two. Draw another square intersecting this one halfway across the top and halfway down. You should end up with five squares, four of which you will be paying attention to.
5
Create a cube out of the two small squares that you just linked. You can do this by drawing lines that connect corresponding points. The top right corner of the first square links with the top right of the second, and so on.
6
Connect the corresponding points on the first two squares as well. You should get a shape that looks like a cube inside of a cube.
7
Tie up loose ends. Draw lines that link corresponding vertices from one cube to the other. Each vertex should have four lines extending from it, although some will not be drawn due to the perspective of the shape.

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Question

Isn't this supposed to be a 5 dimensional shape? This is only 4 dimensions I think.

Community Answer

The introduction at the top clarifies that "A tesseract is a four-dimensional shape." So it is meant to be four dimensional.

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Tips

Although none of the lines will be perfect (even if you use a ruler), a carefully drawn tesseract looks much better than a sloppy one.

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If it helps, draw the shape from a different perspective than the one in the article. Think of the shape like this. To go from a point (0D) to a line (1D) you double the points and connect them. To go from a line and a square (2D) you double the points and connect them again. To get a cube (3D) from a square, you double the points and connect them again. Why should a tesseract (4D) be any different?

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