TABLE OF CONTENTS Countless laws of construction and constitution penetrate matter like secret flashes of mathematical lightning. To equal nature it is necessary to be mathematically and geometrically exact. Number and fantasy, law and quantity, these are living creative strengths of nature; not to sit under a green tree, but to create crystals and to form ideas, that is what it means to be one with nature.
Karel ?apek (1924)
One of the great lessons of condensed matter physics is nature is more fertile than human imagination in devising ways for matter to organize itself into coherent structures. Yet given the initial clue from nature, the human imagination has proved to be remarkably adept at eventually inventing simple theoretical models that display and illuminate strange new kinds of behavior.
D. C. Wright and N. D. Mermin (1989)
For aeons humans have been fascinated by the striking symmetry of many natural objects such as flowers, snowflakes and mineral crystals, and embodied the idea of symmetry in numerous artificial objects such as decoration patterns, handiworks, buildings and monuments. Here is a quote from a passage in a text of ancient China, Peripheral Notes on Poetry by Han Scholars (circa 200 B. C.), "while flowers from plants are mostly fivefold, only snowflakes are sixfold." Perhaps it indicated the first glimmering of consciousness of the subtle difference in symmetry between...
