I'm looking to replicate this spiral pretty much exactly, but with perfect curves etc. using Illustrator. I've tried a few different methods including twist and also just the spiral tool but can't seem to get this exact shape. Any help would be appreciated.
Thanks!
I would redraw over the top of the image manually using the Curvature Tool. You can use extra anchors to try to achieve a more accurate curve as the spiral gets tighter in the middle. It could also be done with the Pen Tool if you are familiar with it.
For example
For more detailed info here's Adobe's help page for the Pen, Curvature, and Pencil tools.
I wasn't aware that AI had a spiral tool, and if it's similar to the same tool in Inkscape, this tutorial video (3:38) for creating the design you seek may be helpful.
Effectively, one creates a duplicate of the first spiral, shrinks it (or expands it) as desired, then joins the spiral origins together and creates a joined line at the outer edge as well. In the video, the outer edge is a straight line, but your objective might require using a segment of a circle to complete the design.
You have already got another answer that says "draw it" and that's the way to quite close replica. Illustrator's spiral isn't an exact replica but with careful settings and gradually widening custom stroke (=art brush) you can make something which can be near enough.
An example: Draw a spiral with the spiral tool:
Make an art brush. I drew a rectangle and moved its top right corner so that the right end height is about 25% of the original. Apply the brush to the spiral:
The brush width is scaled smaller. It's width wasn't designed with measurements.
Draw a circle. Make a copy of it pasted on the same place.
That circle can be used in several ways
In the next image there's no intersection, but the areas are filled with different colors with the Shape Builder and the extra piece is deleted (=hold Alt with the Shape Builder)
I guess your image is a photo of an existing physical spherical piece. To get the 3D look you must add shading and some gloss. It's far from trivial if you expect some plausibility. I skip it.
In a 3D program you can make a model of that piece by subtracting a several turns twisted extruded plane from a spherical surface. Or at least using that plane to define the coloring areas. Illustrator's 3D cannot do it. I have tried it in an older case:
