Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions

Rating:
Summary: Excellent resource for pattern construction
Review: Anyone interested in constructing repeating patterns, the history of design and ornament, quilting, M.C.Escher, geometry, tesselations, or mathematical concepts in the regular division of the plane, will find this hefty book an excellent resource. The historical examples are drawn from an astonishing variety of cultures, and following the exercises at the end of each chapter will give the reader a very thorough grounding in the subject.

Rating:
Summary: A beautiful book on a deep subject
Review: The Handbook of Regular Patterns is 390 pages (plus biblio & index) of lovely black and white images. What ties them together is that they can be repeated to "tile the plane" i.e. to fill an indefinitely large page.

They are broken down into 17 kinds of tilings known as symmetry groups or wallpaper groups, each with its own sort of beauty (the Dutch artist M.C. Escher was well versed in the symmetry groups and used them extensively in his art). As a special bonus, the book also presents the 7 linear groups and a few point groups.

After studying the book for a while I was inspired to design and construct my own regular 2D pattern, a fish shaped tile based on the "p2" symmetry group. I cut about 20 tiles out of stoneware clay and fired and glazed them (over 10 years ago), but I still haven't installed them yet.

I have also used ideas from the book to help design quilting patterns and to make patterns for tile floors (all square tiles, but patterns in groups of tiles). I think the book is a useful item in a designer's toolbox.

An interesting topic not covered in the book (because it's not a true tesselation since it has no repeats) is the penrose tiling. Google for penrose tiling to see beautiful patterns based on pentagonal symmetry.

Rating:
Summary: A beautiful book on a deep subject
Review: The Handbook of Regular Patterns is 390 pages (plus biblio & index) of lovely black and white images. What ties them together is that they can be repeated to "tile the plane" i.e. to fill an indefinitely large page.

They are broken down into 17 kinds of tilings known as symmetry groups or wallpaper groups, each with its own sort of beauty (the Dutch artist M.C. Escher was well versed in the symmetry groups and used them extensively in his art). As a special bonus, the book also presents the 7 linear groups and a few point groups.

After studying the book for a while I was inspired to design and construct my own regular 2D pattern, a fish shaped tile based on the "p2" symmetry group. I cut about 20 tiles out of stoneware clay and fired and glazed them (over 10 years ago), but I still haven't installed them yet.

I have also used ideas from the book to help design quilting patterns and to make patterns for tile floors (all square tiles, but patterns in groups of tiles). I think the book is a useful item in a designer's toolbox.

An interesting topic not covered in the book (because it's not a true tesselation since it has no repeats) is the penrose tiling. Google for penrose tiling to see beautiful patterns based on pentagonal symmetry.