In this copiously illustrated treatise, Conway (mathematics, Princeton) and his colleagues explain the multifold world of symmetries. They begin with an introduction to symmetry starting with the repeating patterns in a kaleidoscope. The many visual examples help the reader in comprehending the methods the authors are using, many of which are a product of their own work. The chapters lead up to the "Magic Theorem" which demonstrates that plane repeating patterns comes in only seventeen types. From planes they move to spheres, folded patterns, Escher-like patterns and Klein bottles. They add the dimension of symmetry of colors to the mix, as well. A firm grounding in non-Euclidian geometry is necessary to truly understand this work but even non-mathematicians can glimpse the way in which the authors explain the symmetry all around us. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)