The reason people would remember the teapot in their head is that they could remember the algorithm to generate it, not necessarily every single point to make a polygon object, but to make, what they call, a Nurb surface object.  Remembering the exact quadratic, sine, cosine mix, to create points along curves to build the teapot.  Makes it a lot easier than remembering every single point on the surface.<br>Math to make art, I love it!