You can simply use the cut extrude and then offset from surface option in that to cut to some depth maintaining the same surface OR even Wrap feature with deboss option.
Does wrap work on doubly-curved surfaces?
NO but that was just a suggestion.
Using this technique, you can get a nice result (how to project icosahedron on a sphere? ) It's a way to wrap it, because I don't think you can wrap on a surface with complex curvature.
On immediate further consideration, you could skip 3 steps by just lofting a cut from the sketch to the origin.
You are right: the wrap feature doesnt work with spherical surfaces. Thanks alot for your help.
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