I remember an online pseudo-IQ test that had an image of an irregular 3D shape with pictographs on it, and then several 2d images of that shape "unfolded" in various different ways, with only one of those unfolded representations being correct and having the right pictographs in the right places at the right rotations.
Does this sound like the kind of test you were asking about?
Mentally visualizing where each side of the shape went when unfolding the shape was important for me in solving those problems, and I think they'd be pretty hard to solve mentally even with intense mastery of abstract algebra.
Previously: Generalizing From One Example
Summary: I do not have visual mental imagery. I want it. How do I get it? What exercises, if any, will help?
In further detail... Here's Francis Galton's Statistics of Mental Imagery paper. I'm not quite at the 3% level of completely unable to form mental images, but I'm close. In particular there are three times I have vivid, sharp mental imagery, and the existence of such times tells me I have the brain hardware to visualize. It's enough to let me know that I want it all the time. Unfortunately I don't know how to get it. And searching online has proven difficult and frustrating... for example this article is first of all about a different meaning of "visualize", it's talking about some kind of self-help motivational thingy, and second of all it starts by saying "How to Visualize: I want you to relax and close your eyes. Picture a hot, sunny day at the beach."
Full Stop. Halt, Catch Fire and Burn.
That's already too far. For those of us who don't visualize, practice definitely does not consist of pulling up mental images, playing with them in new ways, and expanding our imagination. I'm very good at imagination in some ways, but I lack that first ability to pull up a mental image. That's what I want to learn how to have!
Here is a description of what I can do, what I have tried, what I have learned, etc.
I see vivid visual mental imagery in 3 situations: