Color and Symmetry
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 Cover of the 1971 hardback edition | |
| Author | Arthur L. Loeb |
|---|---|
| Subject | Dichromatic symmetry, polychromatic symmetry |
| Publisher | Wiley Interscience |
Publication date | 1971 |
| Media type | |
| Pages | 179 |
| ISBN | 978-0-471-54335-0 |
Color and Symmetry is a book by Arthur L. Loeb published by Wiley Interscience in 1971. The author adopts an unconventional algorithmic approach to generating the line and plane groups based on the concept of "rotocenter" (the invariant point of a rotation). He then introduces the concept of two or more colors to derive all of the plane dichromatic symmetry groups and some of the polychromatic symmetry groups.
The book is divided into three parts. In the first part, chapters 1–7, the author introduces his "algorismic" (algorithmic) method based on "rotocenters" and "rotosimplexes" (a set of congruent rotocenters). He then derives the 7 frieze groups and the 17 wallpaper groups.
In the second part, chapters 8–10, the dichromatic (black-and-white, two-colored) patterns are introduced and the 17 dichromatic line groups and the 46 black-and-white dichromatic plane groups are derived.
In the third part, chapters 11–22, polychromatic patterns (3 or more colors), polychromatic line groups, and polychromatic plane groups are derived and illustrated. Loeb's synthetic approach does not enable a comparison of colour symmetry concepts and definitions by other authors, and it is therefore not surprising that the number of polychromatic patterns he identifies are different from that published elsewhere.
Audience
Unusually, the author does not state the target audience for his book; his publisher, in their dust jacket blurb, say "Color and Symmetry will be of primary interest on the one hand to crystallographers, chemists, material scientists, and mathematicians. On the other hand, this volume will serve the interests of those active in the fields of design, visual and environmental studies and architecture."
Only a school-level mathematical background is required to follow the author's logical development of his argument. Group theory is not used in the book, which is beneficial to readers without this specific mathematical background, but it makes some of the material more long-winded than it would be if it had been developed using standard group theory.[1]
Michael Holt in his review for Leonardo said: "In this erudite and handsomely presented monograph, then, designers should find a rich source of explicit rules for pattern-making and mathematicians and crystallographers a welcome and novel slant on symmetry operations with colours."[2]