> I consider myself on the opposite end of the spectrum from someone who suffers (is blessed?) from aphantasia

One distinct downside is that I'm queasy around other people's blood or gore. I can't watch visceral movie scenes for too long or visit some science exhibits (that I'd otherwise enjoy) because of it (at least this is my suspicion). My problem is that because I can't visualize a discussion about, say, amputation, my mind grafts the description onto me and things go downhill from there. However, I was able to watch some small procedures on myself just fine because I could see that it was OK (though I still cannot watch my own blood being drawn).

> I can muster up not only a mental image of just about anything, but really recreate any sensory experience (although it has a dullness to it) in my head.

Yeah, I don't have anything to compare that to. I recall "gists" of things through feelings and notions rather than anything I'd call "sensory". I cannot recalls scents or tastes all that well and even sounds get muddled up very easily (I have a very hard time finding a rhythm, melody, or other patterns out of music though I can usually pick out instruments while listening; "tap out this song" detectors never worked well for me because I would tap nearly every note and lyric syllable, not some "core" pattern from it).

Some interesting side effects of this include a blank stare while I think about a list of items when someone asks something like "what is your favorite food or drink?". The answer sometimes changes depending on whether I remember "everything" too. Even "what do you think about your travels to X?" brings it up because I have to first conjure up the feelings associated with that travel, remember the big events in that timeline, and then put it into words for the answer (hoping I didn't miss anything).

> What I'm wondering is, how different really are our methods for reasoning about mathematical things, especially the shape rotation/unfolding you mentioned.

The first thing I notice is that I do not "unfold" the possibilities at all; I turn it into a logic puzzle. I focus on one face that is in "most" of the images and look for contradictions with the net by focusing on one or two vertices of that face. Some rules come out of this like "two steps in one axis is an opposing face" and if you see those two symbols on one possibility, it's obviously not a candidate. It also works fine for the harder versions where the symbols on the face are right, but rotated incorrectly to the facing edge. This usually gets you down to one candidate and you can move on to the next one while your hand is filling in the bubble. I suspect (but have no actual experience with it as most of such tests are on cubes) this scales up well for even octahedra and dodecahedra (but starts to fall apart trying to keep the order/orientation of the 5 items around a vertex for an icosahedron or when the possibilities do not share many symbols from their view because that greatly slows down the method). Giving "adversarial" nets where the answer is actually based on two distant legs of the net that I need to actually mentally fold multiple edges also likely stymies my strategy because I have to think "star circle square" as I walk the edges and cannot just "snap" a picture of the sequence as a gestalt as easily.

I took part in a research experiment recently where they have some 3d shapes made of cubes rotated around a vertical axis and ask "are these two objects the same or mirror images of each other". I obviously don't have the answer key, but I felt that I did really well except when mirror images were rotated 180° from each other. I don't know if I have an explanation for that (usually I realized my mistake right after answering).

> If that were the case, I'd argue aphantasia is an advantage, as you're not bothering your brain with unnecessary work.

I think a major difference is in working memory. What you might be able to "freeze frame" as a collection, I have to extract out the distinct parts and remember them more individually. Sometimes I can "find" a pattern and gestalt that way which tends to stick quite well (like I do for my wife's phone number or a friend's phone number I saw a pattern in once he got it), but most things are just rote memorization.

For example, "star square circle" could just be "decreasing side counts" and just using recognition to determine membership later versus "star circle square" which is more likely to be 3 working items. If they are also colored, that doubles the work for me right away as they otherwise don't have any color association to me.