From: The World In Your Head by Steven Lehar

Fig. 6.5 A cube can be abstracted to its plane faces that bound the volume of the cube. Those faces can be further abstracted to the straight lines that bound them. The lines can also be abstracted to the pair of points that bound their endpoints at the vertices of the cube, and finally the pattern of vertices can be abstracted to an eightfold pattern of vertices about a center of symmetry. That eightfold symmetry encodes the cubical form, independent of rotation, translation, or scale.