Kepler's essay, On the Six-Cornered Snowflake, provides the first published evidence of the ideas of regular arrangements and close-packing which have proved fundamental to crystallography. In it, Kepler ponders on the problem of why snowflakes are hexagonal, two centuries before the first successful steps were taken towards its solution. The purpose of this volume is to display the historical, literary, scientific, and philosophical treasures of Kepler's essay. The book includes the modernized text of the 1611 Latin edition, with an English translation by Colin Hardie on the opposite pages. The text is accompanied by an introduction giving details of the history of the work, and two essays; Professor B. J. Mason's discussion of the scientific meaning and validity of Kepler's arguments and their relation to the history of crystallography and of space filling, and L. L. Whyte's examination of Kepler's facultas formatrix in relation to the history of philosophical and scientific ideas on the genesis of forms.