Seemingly Unnamed Toroid(?) Structure

[Anchovyforestbane]

Is there a specific name for this 3D shape, which appears to be an elliptical torus twisted into a sort of spiral?

Additionally, how would one go about graphing a structure like this?

Edited September 11, 2020 by Anchovyforestbane

[Dubbelosix]

That's a Torus in four dimensions, i think.

Edited September 13, 2020 by Dubbelosix

[Turtle]

That s a Torus in four dimensions, i think.

If so, then I think it's a Klein bottle. :Lightbulb

[Anchovyforestbane]

That's a Torus in four dimensions, i think.

No, I'm pretty sure it's not. Here's a little more information on the 4D equivalent of a torus.

https://dr-mikes-maths.com/4d-torus.html

 

 

If so, then I think it's a Klein bottle. :lightbulb

The shape displayed above is most certainly not a Klein bottle, although it likely could be given the correct translation function.

Example of a Klein bottle ^^^

[Turtle]

http://virtualmathmuseum.org/Surface/klein_bottle/klein_bottle.html

[Turtle]

http://virtualmathmuseum.org/Surface/klein_bottle/klein_bottle.html

There exist several forms of Klein bottles as explained at link. Whether the torus in OP IS a Klein bottle or not, it looks like one variation as below from the link.

[Anchovyforestbane]

There exist several forms of Klein bottles as explained at link. Whether the torus in OP IS a Klein bottle or not, it looks like one variation as below from the link.

Very, very interesting... I wouldn't be eager call this shape a type of Klein bottle, given that, as is detailed in the information you've sent me, the shape is translated from one half of a symmetrical Klein bottle. However, I am incommunicably fascinated by a Klein bottle's ability to become a Mobius strip, and then by extent this strange mystery shape, so I thank you for introducing me to this information.

Additionally, it is hard to say this shape is the same, as the OP is completely circular, whereas this one is not quite. But perhaps it is close enough, we shall see.

Edited September 14, 2020 by Anchovyforestbane

[Turtle]

I am incommunicably fascinated by a Klein bottle's ability to become a Mobius strip, and then by extent this strange mystery shape, so I thank you for introducing me to this information.

You're welcome. :)

it is hard to say this shape is the same, as the OP is completely circular, whereas this one is not quite. But perhaps it is close enough, we shall see.

My first impression when you posted was an inflated Möbius strip. Thanks for an interesting diversion in any regard.

[Dubbelosix]

Its difficult to discern here whether this toroid is expressed in four dimensions, albeit, I did not even think of a Klein bottle.

[Dubbelosix]

The simplest four dimensional analogue looking up now, has a structure similar but not exact https://www.google.com/search?q=torus+in+four+dimensions&client=ms-android-zte&sxsrf=ALeKk02R9ZI67UP4j7NqERRrKCnKZkHmxQ:1600207395653&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiY1ImLlezrAhWLQc0KHfKxC8EQ_AUIBigB&biw=320&bih=399#&biw=320&bih=399