We present a formal description of `Face Fundamental Transversals' on the faces of the Complexes of polyhedra (meaning threedimensional polytopes). A Complex of a polyhedron is the collection of the vertex points of the polyhedron, line segment edges and polygonal faces of the polyhedron. We will prove that for the faces of any 3-dimensional complex of a polyhedron under face adjacency relations, that a `Face Fundamental Transversal' exists, and it is a union of the connected orbits of faces that are intersected exactly once. While exploring the problem of finding a face fundamental transversal, we have found a partial result for edges that are incident to faces in a face fundamental transversal. Therefore we will present this partial result, as The Edge Transversal Proposition 1. We will also discuss a few conjectures that arose out this proposition. In order to reach our approaches we will first discuss some history of polyhedra, group theory, and incorporate a little crystallography, as this will appeal to various audiences.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-4941 |
| Date | 01 January 2011 |
| Creators | D'Andrea, Joy |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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