# Turning a torus inside out. Possible in the real world? **URL:** \ **Category:** Factual Questions\ **Created:** [June 17, 2023, 8:21pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694 "2023-06-17T20:21:11Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Zyada](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zyada/32/3028_2.png) [@Zyada](https://boards.straightdope.com/u/Zyada)\ **Post date:** [June 17, 2023, 8:21pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/1 "2023-06-17T20:21:11Z")
I have a small needlepoint project that I never finished. It’s a wreath, front and back. To finish it, I would sew it so that the stitched sides are together, leaving a small section unstitched, then turn it inside out, stuff it, and sew the final section. But every time I think of trying to turn a torus inside out, I am stymied. If it’s possible, where do I join the pieces? Or is it impossible?! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 17, 2023, 8:32pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/2 "2023-06-17T20:32:17Z")
It is possible, if the material it’s made from is flexible enough, and an inside-out torus is also a torus. But the catch is that the hole isn’t the same hole any more. Your wreath is probably shaped more or less like a long tube, wrapped around a circle, and with the ends connected, right? Well, now picture that that long tube is like a sock, and turn it halfway inside out like you would a sock, and connect the ends together. If that’s not clear enough, I can try to draw a picture. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [June 17, 2023, 8:40pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/3 "2023-06-17T20:40:00Z")
Here’s an animation. Note that the orientation of the stripes is different at the end. [https://twitter.com/i/status/886936289496510466](https://twitter.com/i/status/886936289496510466) ---
**Author:** ![Zyada](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zyada/32/3028_2.png) [@Zyada](https://boards.straightdope.com/u/Zyada)\ **Post date:** [June 17, 2023, 8:42pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/4 "2023-06-17T20:42:50Z")
Those are cool! I might have to do something similar, although I won’t be able to do it with this project - nowhere near stretchy enough! ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [June 18, 2023, 3:37pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/5 "2023-06-18T15:37:07Z")
> [@Chronos](#): > > But the catch is that the hole isn’t the same hole any more. The way I’vehad this explained is that the hole that was the “doughnut hole” of the inner tube becomes the space for the air inside the inner tube, and where the air was, becomes the hole. ---
**Author:** ![pjd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pjd/32/3009_2.png) [@pjd](https://boards.straightdope.com/u/pjd)\ **Post date:** [June 18, 2023, 6:27pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/6 "2023-06-18T18:27:23Z")
The problem is, you violate the laws of topology when you turn a torus inside out. See [here](http://geofhagopian.net/papers/GARDNER01.pdf#page=155) for details. (starts halfway down the page.) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 18, 2023, 9:27pm UTC](https://boards.straightdope.com/t/turning-a-torus-inside-out-possible-in-the-real-world/985694/7 "2023-06-18T21:27:29Z")
You also violate the laws of topology when you make the torus to begin with. We’re talking about sewing, here, not topology.