How to Draw a 4D Hypercube (My Way)

Updated on November 13, 2017
"In geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube."
"In geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube."

A Tesseract Is a Four Dimensional Hypercube

If you're drawing a square on a flat sheet of paper, how many straight lines does it take? Four. If you're drawing a cube, how many squares (sides) does that take? Six. So if you're drawing a tesseract, how many cubes does that take? Eight!

In this article, I'm going to show you how to draw your very own tesseract! The lengths of the lines and the angles won't be exact, however, because I'm not using a ruler for this tutorial.

Step 1
Step 1

First: How to Draw an Ordinary Cube

Step 1: Draw two lines of equal length, attempting to keep them an equal space apart, at slightly different heights.

Step 2
Step 2

Step 2: Connect the two lines as shown, creating what looks like a smooshed square, or a fat diamond that fell over.


Step 3
Step 3

Step 3: Draw four parallel lines stemming from each of the shape's four corners.


Step 4
Step 4

Step 4: Connect the ends of the two top lines, the ends of the two bottom lines, and then connect each bottom line with the line above.

Visual instructions for drawing the tesseract follow below:

Step 5
Step 5
Step 6
Step 6
Step 7
Step 7
Step 8
Step 8
Step 9
Step 9
Step 10
Step 10
Step 11
Step 11
Step 12
Step 12
Step 13
Step 13
Step 14
Step 14
Step 15
Step 15
Step 16
Step 16
Step 17
Step 17
Step 18
Step 18
Step 19
Step 19
Step 20
Step 20
Step 21
Step 21
Step 22
Step 22
Step 23
Step 23

And there you have it! A complete two dimensionally rendered tesseract, and only twenty-three steps later. I hope you enjoyed my little tutorial!

If you're interested to learn more about four dimensional geometry, try getting your hands on a copy of Geometry, Relativity, and the Fourth Dimension by Rudolf v. B. Rucker, published in 1977.

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      Fourdimensional 3 weeks ago

      Rotation in four-dimensional space.

      https://youtu.be/vN9T8CHrGo8

      The 5-cell is an analog of the tetrahedron.

      https://youtu.be/z_KnvGGwpAo

      Tesseract is a four-dimensional hypercube - an analog of a cube.

      https://youtu.be/HsecXtfd_xs

      The 16-cell is an analog of the octahedron.

      https://youtu.be/1-oj34hmO1Q

      The 24-cell is one of the regular polytope.

      https://youtu.be/w3-TqPXKlVk

      The hypersphere is an analog of the sphere.

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      jimmy 3 months ago

      The steps are a little difficult to memorize.

    • profile image

      BlahBlah 8 months ago

      My Wrinkle in Time project will be much easier now. THX

    • profile image

      Alex 2 years ago

      Hi! its me again i just found one little error. You know how you highlight your next line? Well, on Step 12 you highlighted the line you highlighted last step on step 11. I hope that wasn't too confusing! Thank you for your time!

    • profile image

      Alex 2 years ago

      wow! thank you so much! i just love the looks of the 4D Hypercube! Its just so cool!

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