The generalized cone in human spatial organization

The generalized cone is one of the newer concepts useful for describing spatial structures, and it has become popular as a volumetric primitive in models of object recognition. Apart from this use of the concept (or perhaps underlying it), the generalized cone can be considered a species of spatial regularity. In the general definition of symmetry as invariance across transformation, the generalized cone is a combination of translation and dilation symmetry. In such symmetry, there is homogeneity both of the slants of edges and surfaces of an object about an axis and the radial positions of these features about the axis. The results of two research projects are reviewed suggesting that the generalized cone is useful in human spatial organization. In the first instance, each of the three simpler regular polyhedra, the Platonic Solids, are easiest to perceive and imaging when they are organized as generalized cones. In the second instance, people imagine simple rotations best when the symmetric space that would be traced by the motion is aligned with salient spatial reference systems.