Orbit Systems

Abstract

In this chapter, some geometrical application possibilities of the realization theory in the previous chapter will be explained. It will be shown how different sorts of polyhedral symmetric shapes are actually associated with realizations of groups of isometries. According to the given definitions, a group realization implies a homogenous space isomorphism between a right G-set and the orbit of the descriptive. The right G-set is determined by the stabilizer of the positioned descriptive. Examples of descriptives will be restricted to space-(l) bodies, whereas in Chapter 6, some attention will be also dedicated to higher-level descriptives. Two distinct categories occur on level (1): point singletons and sets of more points.