Symmetry makes things predictable. That’s why cubes are boring shapes for designers. Rotate them along 13 different axes and you will see the same thing. I designed a set of wood and 3D-printed blocks based on a special geometry that is surprisingly asymmetrical - the parallelepiped. While it looks like a cube it behaves differently from one when you manipulate it.
I have exploited these perceptual properties for conducting interaction experiments throughout my studies. With them we can study how designers think with their hands to reshape their environment and see things in new ways.