THIS WORK IS DEDICATED TO H. S. M. COXETER PROFESSOR OF MATHEMATICS UNIVERSITY OF TORONTO To me no experience of childhood so reinforced self- confidence in one’s own exploratory faculties as did geometry. Its inspiring effectiveness in winnowing out and evaluating a plurality of previously unknowns from a few given knowns, and its elegance of proof lead to the further discovery and comprehension of a grand strategy for all problem solving. By virtue of his extraordinary life’s work in mathematics, Dr. Coxeter is the geometer of our bestirring twentieth century, the spontaneously acclaimed terrestrial curator of the historical inventory of the science of pattern analysis. I dedicate this work with particular esteem for him and in thanks to all the geometers of all time whose importance to humanity he epitomizes.