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Fundamental Transversals On The Complexes Of Polyhedra, Joy D'Andrea
Fundamental Transversals On The Complexes Of Polyhedra, Joy D'Andrea
USF Tampa Graduate Theses and Dissertations
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 …