I know how to make a sphere with 2 circles and Follow Me.

I have created a model with 24 vertices (based off a cuboctahedron, with circular faces perpendicular to the line that runs from the center of the model to the vertice. See attached.

What I would like to do is have these faces mapped onto a sphere, so that the edges of the circles touch the edge of the sphere (center to circle edge = radius of sphere), but the dome that would be above the circle is flattened to the vertice - so we end up with a sphere with 24 flat spots on it.

I used the Soap Skin & Bubble plugin to create each of those components.
I reversed the faces of those components just to be visible in the first phase, otherwise they must be turned, with a visible white face, like circles.

And did you follow any youtube tutorial to understand how the SSB plug-in works?
Also, look carefully at my model to see how I created that area of the sphere, dividing it into areas.

You could intersect a sphere with the faces at the right dimension and remove the excess.
The faces donâ€™t need to be round, and the more detail in the sphere the rounder the result.

Iâ€™m struggling with this. Iâ€™ve scaled my original model up massively, but every time I try this, the intersected faces donâ€™t have the nice round edge profiles that yourâ€™s do. What am I doing wrong? 24 side scaled by 10000000.skp (1.3 MB)

Itâ€™s not the size itâ€™s the detail.
Here it is with a sphere made from 2 circles with 96 segments.
But remember the more segments the larger the file.