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.

Questions & Answers

    Comments

      0 of 8192 characters used
      Post Comment

      • profile image

        Fourdimensional 

        10 months 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.

      • profile image

        jimmy 

        12 months ago

        The steps are a little difficult to memorize.

      • profile image

        BlahBlah 

        17 months ago

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

      • profile image

        Alex 

        3 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 

        3 years ago

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

      working

      This website uses cookies

      As a user in the EEA, your approval is needed on a few things. To provide a better website experience, feltmagnet.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

      For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://feltmagnet.com/privacy-policy#gdpr

      Show Details
      Necessary
      HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
      LoginThis is necessary to sign in to the HubPages Service.
      Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
      AkismetThis is used to detect comment spam. (Privacy Policy)
      HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
      HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
      Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
      CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
      Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
      Features
      Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
      Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
      Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
      Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
      Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
      VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
      PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
      Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
      MavenThis supports the Maven widget and search functionality. (Privacy Policy)
      Marketing
      Google AdSenseThis is an ad network. (Privacy Policy)
      Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
      Index ExchangeThis is an ad network. (Privacy Policy)
      SovrnThis is an ad network. (Privacy Policy)
      Facebook AdsThis is an ad network. (Privacy Policy)
      Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
      AppNexusThis is an ad network. (Privacy Policy)
      OpenxThis is an ad network. (Privacy Policy)
      Rubicon ProjectThis is an ad network. (Privacy Policy)
      TripleLiftThis is an ad network. (Privacy Policy)
      Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
      Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
      Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
      Statistics
      Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
      ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
      Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)