This well-illustrated book—in color throughout—presents a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.

Reviews

I have loved the beauty and symmetry of polyhedra and spherical divisions for many years. My own efforts have been concentrated on making both simple and complex spherical models using classical methods and simple tools. Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include Computer-Aided Design and applications, which I would never have imagined when I started down this fascinating and rewarding path.

His lovely illustrations bring the subject to life for all readers, including those who are not drawn to the mathematics. This book demonstrates the scope, beauty and utility of an art and science with roots in antiquity. Spherical subdivision is relevant today and useful for the future. Anyone with an interest in the geometry of spheres, whether a professional engineer, an architect or product designer, a student, a teacher, or simply someone curious about the spectrum of topics to be found in this book, will find it helpful and rewarding.

—Magnus Wenninger, Benedictine Monk and Polyhedral Modeler

Edward Popko’s Divided Spheres is the definitive source for the many varied ways a sphere can be divided and subdivided. From domes and pollen grains to golf balls, every category and type is elegantly described in these pages. The mathematics and the images together amount to a marvelous collection, one of those ks that will be on the bookshelf of anyone with an interest in the wonders of geometry.

—Kenneth Snelson, Sculptor and Photographer

Edward Popko’s Divided Spheres is a ‘thesaurus’ must to those whose academic interest in the world of geometry looks to greater coverage of synonyms and antonyms of this beautiful shape we call a sphere. The late Buckminster Fuller might well place this manuscript as an all-reference for illumination to one of nature’s most perfect invention.

—Thomas T.K. Zung, Senior Partner, Buckminster Fuller, Sadao & Zung Architects

My own discovery, Waterman Polyhedra, was my way to see hidden patterns in ordered points in space. Ed's book Divided Spheres is about patterns and points too but on spheres. He shows you how to solve practical design problems based spherical polyhedra. Novices and experts will understand the challenges and classic techniques of spherical design just by looking at the many beautiful illust...