# What is a tesseract? **URL:** \ **Category:** Factual Questions\ **Created:** [February 21, 2003, 4:06am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475 "2003-02-21T04:06:04Z")\ **Posts on this page:** 7\ **Page:** 2
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 23, 2003, 3:59am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/21 "2003-02-23T03:59:27Z")
Robert Heinlein does a good job of describing a tesseract in his short story “And He Built a Crooked House”. You can read it [here.](http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html) ---
**Author:** ![Barking\_Dog](https://avatars.discourse-cdn.com/v4/letter/b/ccd318/32.png) [@Barking\_Dog](https://boards.straightdope.com/u/Barking_Dog)\ **Post date:** [February 23, 2003, 6:42am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/22 "2003-02-23T06:42:01Z")
[slight hijack] I wonder, what would a 4th dimension sphere be like? Would it be called a hyper-sphere or some such? What about a hyper-pyramid or cone? * * * “I madam, I made radio! So I dared! Am I mad? Am I?” ~Nikola Tesla ---
**Author:** ![Speaker\_for\_the\_Dead](https://avatars.discourse-cdn.com/v4/letter/s/c77e96/32.png) [@Speaker\_for\_the\_Dead](https://boards.straightdope.com/u/Speaker_for_the_Dead)\ **Post date:** [February 23, 2003, 7:01am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/23 "2003-02-23T07:01:46Z")
Well, isn’t a sphere just an infinite number of 2D circles around a single point? ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [February 23, 2003, 7:21am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/24 "2003-02-23T07:21:08Z")
Yes, 4D sphere would be called a hyper-sphere. Just like the lower dimensional circle and sphere, it would be all the points a fixed distance from the center, but in a 4D space. Its hyper-surface would be 3-dimensional – unbounded yet finite 3-dimensional space. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 23, 2003, 5:03pm UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/25 "2003-02-23T17:03:11Z")
> [@](#): > > \*Originally posted by Barking Dog \* > **What about a hyper-pyramid or cone?** It’s a little tough for me to imagine exactly what these would be like, but without a doubt they can exist. You might google for “hyper-cone” to see what you can find. ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [February 24, 2003, 3:20am UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/26 "2003-02-24T03:20:09Z")
I think we can come up with reasonable definitions for hyper-cone and hyper-pyramid. A hyper-plane is a commonly defined as a 3D space imbedded in a 4D space. A (3D) sphere lies entirely in some hyper plane. Take a sphere in 4D space. From the center of the sphere, draw a line that is perpendicular to the hyper-plane that contains the sphere. Pick a point on this line; we’ll call this point the apex. A hyper-cone will be all of the lines connecting the apex to points on the sphere. A hyper-pyramid could be defined similarly using a cube as the base. ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [February 24, 2003, 2:45pm UTC](https://boards.straightdope.com/t/what-is-a-tesseract/156475/27 "2003-02-24T14:45:33Z")
Not only is that definition reasonable, it’s actually quite commonly used… [Previous page](https://boards.straightdope.com/t/what-is-a-tesseract/156475.md?page=1)