Appendix A - 5 pages Tables of the groups used in the thesis, along with some numerical information and diagrams. Appendix B - 6 pages An example of a combinatorially regular polytope with Schlafli Symbol {4|3|..|3|4} which is nonetheless not a lattice, and a proof that all flag regular polytopes with this Schlafli Symbol are lattices. Appendix C - 5.5 pages Some CAYLEY programs which get mentioned in Chapter 6.