Thesis Info

Thesis Title
A New Approach in the Visualisation of the Six Regular Polytopes*
Chris Foster
2nd Author
3rd Author
Number of Pages
Leeds Metropolitan University
Thesis Supervisor
Reinhold Behringer
Supervisor e-mail
r.behringer AT
Other Supervisor(s)
Sean Wilcock
Language(s) of Thesis
Department / Discipline
Computing and Creative Technology
Languages Familiar to Author
URL where full thesis can be found
Vector Graphics, Design, Four Dimensions, Wireframe, Polytope, Geometry
Abstract: 200-500 words
Using vector graphic software and a stepping process with four dimensional geometry, one can see into the nature of complex structures. This method of stepping has the advantage over single models, diagrams, animations of the Polytope in that it simplifies and deconstructs the Polytope into its constituent parts. For example, the Hypercube, 8 Cell, has eight three dimensional cubes, cells, in one hypercube of four dimensions. By stepping the Hypercube using vector graphic "wireframe" software eight times one can see the individual highlighted single cell, its position and orientation through the four dimensional polytope – this stepping method is unique, and is not seen in individual models. Furthermore, there have been recent scientific developments, particular with the single modelled Hypercube, examples of these single models are compared and analysed in this thesis with the stepping process of the Hypercube. The stepping method applies for the remaining five regular, of equal length and angle, Polytopes, the 5, 16, 24, 120 and 600 Cell. Completion of the practice work has resulted in the production of a DVD, this contains vector graphic work in PDF format, JPG's and technical data of the stepped six regular polytopes plus one stepped non convexed, of intersecting edges, polyhedra. Specifically this thesis offers a clear and visual insight into a complicated subject matter – four dimensional geometry. Also, contextually being multidiscipline in structure, this visual and mathematical deconstruction of the stepped polytopes is useful for scholars from various fields, besides mathematics and geometry, artistic and scientific who would want to gain knowledge. Besides the aesthetic and abstract beauty of stepping the Polytope this novel and alternative method may be useful additionally in further understanding complex surfaces, mapping and topology. *Polytope or Hypersolid (of four dimensions), theoretically a four dimensional Polyhedra – hierarchy one has Polygon, Polyhedra and Polytope or two, three and four dimensions .