The regular polyhedra, commonly known as the "Platonic solids", are fundamental three-dimensional structures. It is known that the ease of imagining one of these solids, the cube, varies radically with
its orientation to the vertical. We demonstrate the same variation for perception and imagination of all three of the simpler Platonic solids: The cube, octahedron, and tetrahedron. In orientations of the
objects that are relatively easy to comprehend, the objects are generalized cylinders about the vertical. In the difficult orientations, the objects are antiprismatic about the vertical. The critical difference
between these structures is that generalized cylinders have uniform orientations of edges and surfaces about an object axis while antiprisms have nonuniform orientations. These results support strongly
the view that the orientations of objectfeatures are important in spatial organization, that humans are highly sensitive to objective forms of regularity in spatial organization, and that the generalized
cylinder is a form of spatial regularity that people find simple.