(First of all, I'm a new member, so I apologize in advance. Not for anything specific; just, you know, a generalized preemptive apology.)

I am driving myself nuts, because I'm trying to find an image of a type of antique global projection map that could swear I've seen dozens of times, and honestly thought was as common as muck, until I started trying to find images of it! Perhaps I imagined it, or perhaps it's not a 'real' type of projection, but rather something made up by talented fantasy novel illustrators, and therefore harder to find by way of Google image search. Whatever it is, it's the style I'd like to use for my own fake map of a fake world, but I'd desperately like to look at a few examples of the same style before I waste time trying to recreate a vague memory.

I'm not great with cartographic terminology, and most of what I know I've learned only in the last few hours, so see above re: multi-purpose apology.

However, I'll try to describe my vague memory. What I'm remembering is a type of interrupted projection, if I'm using the term correctly. If you can, imagine a cross between the orange peel / Goode homolosine type of projection, and the renaissance globular stereographic hemisphere maps. In other words, interrupted into segments, but segments with circular edges, kind of like this:
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but perhaps interrupted in a different way, and definitely better, more graceful, and done in a Ye Olde style. If that makes sense.

The more I look for an example, the more I think I must have imagined the whole thing! Can anyone point me to any example of this style of projection, from any source at all?