I am new to the term aphantasia as well. I always thought people were just using a phrase “picture this” in the abstract, not that they were actually visualizing an apple or a sunset or whatever. In yoga The instructor will always talk about images, and I never realize that the other people in the class probably were seeing a beach or clouds or something. Anyway, I am an artist and I can not visualize things so I draw everything I think about in order to not only capture it, but to also work out the facets of construction, etc.
My question to you pertains to this geometric thing you are describing. I think I have a similar mode of imagining. I also have a way of making things in my mind that is really hard to describe, but it is as if I have dark gray/black powder/dust/chalk and I am not touching it, but my mind is moving it in 3 dimensions as a feeling, not an image. I never knew this was not how everyone thinks until recently. At first I thought it was like dark smoke, but as I concentrate I feel it has dimension/substance. I wonder if anyone else knows what I am saying. In reading posts I see a lot of different ways of conceiving things in the mind that does not involve an image, but my particular variant does not seem to be described by anyone else.