Polyhedric configurations.

Polyhedra have been the subject of fascination and interest to mathematicians, philosophers and artists since the ancient times. Forms based on polyhedra have subsequently become popular with engineers and architects. However, data generation for these polyhedric configurations has traditionally been a barrier to advancement in this area. Graphical based solutions have been applied which have severely limited the scope of the applications. The objective of the present work is to facilitate the creation of forms based on polyhedral, and so broaden the boundaries as to what is achievable. To this end the work is concerned with the development and implementation of the concepts in a computer based environment. In order for this to be achieved three key elements are required for each polyhedron. They are as follows; o Establishment of a coordinate system, o Evolution of a set of conventions for assigning identity numbers for faces, edges and vertices of polyhedra, and o Establishment of an orientation system for mapped objects. These have been developed to be compatible within the computer based environment. The implementation of the concepts is through the 'polymation function', which has been created to be a standard function within the programming language Formian. A series of other functions, complementary to the polymation function have been developed to be used within Formian. The most prominent of these is the 'tractation function' which is used to project configurations onto a range of surfaces, including a user-defined surface. The work includes a look at some of the forms which may be created using the new tools, particularly in the area of 'geodesic' forms. Suggestions for future research in this field include widening the range of polyhedra available, looking at the problem of 'mitring', exploring rendering techniques and the development of a more general function which could encompass user-defined polyhedra