A Thought Experiment

[Siegmund]

As long as you are receiving SOME kind of input to your brain, telling a sphere from a non-sphere is extremely easy: if it looks different when viewed (or touched, or anything-elsed) from different angles, it is a non-sphere.

If you asked someone to tell a cube from a pyramid, they might be fooled since they'd have to pay attention to what side they were looking at and how sharp the points were. Asked them to tell a regular octahedron from two square pyramids of a different b/h ratio glued base to base, or even an octahedron from a cube standing on its point, and you might well challenge them.

Incidentally, as far as identifying symmetry elements of somewhat obscure shapes goes - sighted people find this task much easier if they can handle a model, and easier still if they can mark the outside of the model with chalk, than if they have to do it by sight alone. (Abstract algebra teachers take note! I learned more about space groups from my mineralogy course in the geology department than I did in the math department! We actually had such models... a set of wooden blocks, between 50 and 100 of them, for all the common crystal shapes. I borrowed them as props for a seminar in the math department once and had a very warm reception.)