Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, and a key figure in the development of quantum physics and general relativity. He was a member of the Institute for Advanced Study in Princeton and the author of many books.

"This short book on a vast subject is the work of a master. With a few sure and authoritative words [Weyl] gives us the heart of the matter. There is no book ... quite like this one on the subject of symmetry and I doubt if any book will be written in the future that will not in some way lean upon this one... [I]t contains so much besides mathematics that it can still be read with profit and enjoyed by someone who has not advanced beyond long division."--John Tyler Bonner, Science "Dr. Weyl presents a masterful and fascinating survey of the applications of the principle of symmetry in sculpture, painting, architecture, ornament, and design; its manifestations in organic and inorganic nature; and its philosophical and mathematical significance."--Scientific American "Weyl offers deep insight into [the concept of symmetry], its foundations in group theory, its applications in physics, chemistry, and biology, and its role in art."--Manfred Eigen and Ruthild Winkler in Laws of the Game "Vivid and picturesque... [Weyl is] an outstanding thinker."--Wolfgang Yourgrau, Philosophy and Phenomenological Research

• Bilateral symmetry 3 Translatory, rotational, and related symmetries 41 Ornamental Symmetry 83 Crystals. The General mathmatical idea of symmetry 119 Appendices A. Determination of all finite groups of proper rotations in 3-space 149 B. Inclusion of improper rotations 155 Acknowledgements 157 Index 161

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, and a key figure in the development of quantum physics and general relativity. He was a member of the Institute for Advanced Study in Princeton and the author of many books.

"This short book on a vast subject is the work of a master. With a few sure and authoritative words [Weyl] gives us the heart of the matter. There is no book ... quite like this one on the subject of symmetry and I doubt if any book will be written in the future that will not in some way lean upon this one... [I]t contains so much besides mathematics that it can still be read with profit and enjoyed by someone who has not advanced beyond long division."--John Tyler Bonner, Science "Dr. Weyl presents a masterful and fascinating survey of the applications of the principle of symmetry in sculpture, painting, architecture, ornament, and design; its manifestations in organic and inorganic nature; and its philosophical and mathematical significance."--Scientific American "Weyl offers deep insight into [the concept of symmetry], its foundations in group theory, its applications in physics, chemistry, and biology, and its role in art."--Manfred Eigen and Ruthild Winkler in Laws of the Game "Vivid and picturesque... [Weyl is] an outstanding thinker."--Wolfgang Yourgrau, Philosophy and Phenomenological Research

• Bilateral symmetry 3 Translatory, rotational, and related symmetries 41 Ornamental Symmetry 83 Crystals. The General mathmatical idea of symmetry 119 Appendices A. Determination of all finite groups of proper rotations in 3-space 149 B. Inclusion of improper rotations 155 Acknowledgements 157 Index 161

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, and a key figure in the development of quantum physics and general relativity. He was a member of the Institute for Advanced Study in Princeton and the author of many books.

"This short book on a vast subject is the work of a master. With a few sure and authoritative words [Weyl] gives us the heart of the matter. There is no book ... quite like this one on the subject of symmetry and I doubt if any book will be written in the future that will not in some way lean upon this one... [I]t contains so much besides mathematics that it can still be read with profit and enjoyed by someone who has not advanced beyond long division."--John Tyler Bonner, Science "Dr. Weyl presents a masterful and fascinating survey of the applications of the principle of symmetry in sculpture, painting, architecture, ornament, and design; its manifestations in organic and inorganic nature; and its philosophical and mathematical significance."--Scientific American "Weyl offers deep insight into [the concept of symmetry], its foundations in group theory, its applications in physics, chemistry, and biology, and its role in art."--Manfred Eigen and Ruthild Winkler in Laws of the Game "Vivid and picturesque... [Weyl is] an outstanding thinker."--Wolfgang Yourgrau, Philosophy and Phenomenological Research

• Bilateral symmetry 3 Translatory, rotational, and related symmetries 41 Ornamental Symmetry 83 Crystals. The General mathmatical idea of symmetry 119 Appendices A. Determination of all finite groups of proper rotations in 3-space 149 B. Inclusion of improper rotations 155 Acknowledgements 157 Index 161