Constructing Hyperbolic Polyhedra using Newton's Method
Roland Roeder
University of Toronto
December 4, 2006
Abstract: This talk has three
parts. In the first part I will explain the statement of
Andreev's classification theorem for compact 3-dimensional hyperbolic
polyhedra (whose dihedral angles are non-obtuse).
In the second part I will explain how the proof of Andreev's Theorem
provides for an algorithm that, in combination with Newton's Method,
can be used to construct hyperbolic polyhedra. I will then
demonstrate the program.
In the third part I will present experimental data such as length
spectra and volumes obtained by using SnapPea to study some polyhedral
orbifolds constructed using my program.
If there is time remaining I will outline two potentially interesting
further experiments.