I first learned about Sphere Spirals back in 2002 via a POV-Ray Hall Of Fame entry by Tor Olav Kristensen. The entry points to a nice mathematical write-up of the underlying idea. (source code for the original work)

In this post, I’ll show one way to build a similar object in Blender. Blender is a free, open source, 3D modeling software that runs on most platforms. My approach isn’t mathematically exact, but visually it’s very similar.

Step 1. Start with a UV Sphere. 8 segments. 8 rings. 1m radius (you can use other units if you prefer).

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Step 2. Enter object edit mode and select the faces to keep. I like to remove the top and bottom faces to cut a hole at each pole. You can experiment by keeping or removing different sets of faces.

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Step 3. Invert the selection.

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Step 4. Delete the faces. We are now left with a single band.

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Step 5. Add the “Array” modifier. We want the shape to be a circle. Set the count to 4. Pick the Z axis. Enable merge. We now have 4 bands forming a sphere.

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Step 6. Add the “Solidify” modifier. 0.1m thickness. Offset shouldn’t matter, I set it to 0.

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Step 7. Add “Simple Deform” modifier. 90degrees around the Z axis. Things are starting to look good.

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Step 8. Add “Subdivision Surface”, pick levels 3-5 depending how smooth you want the sphere to look.

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That’s it. The order of the modifiers is important. If things don’t look quite right, re-order the modifiers. You can also generate a UV sphere with a multiple of 6 and have 3 bands instead of 4 (or try other numbers).

These little spheres are fun to 3D print and turn into keychains. You can also make lamp shades. Leave the bottom filled to make a candle stand. Leave a complete opening at the top and pair two for a fidget toy.

via https://www.printables.com/model/973881-fidget-spiral-sphere

via https://www.etsy.com/ca/listing/1802486916/hand-blown-glass-globe-pendant-light