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Orbit Systems

  • Hugo F. Verheyen
Part of the Design Science Collection book series (DSC)

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.

Keywords

Symmetry Group Finite Group Orbit System Regular Polygon Threefold Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Hugo F. Verheyen
    • 1
  1. 1.AntwerpenBelgium

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