How to Polygon: Art and Geometry of Plane Tiling by Mike Regan
Mike Regan, to quote his own bio, “is a geometer who takes his subject seriously.” So seriously that, along with colleagues, friends and family, he mentions the ancient Greeks Pythagoras and Euclid in the opening acknowledgments of his fascinating instructional book, How to Polygon: Art and Geometry of Plane Tiling (Archway Publishing).
Don’t be intimidated by the title. And no, we didn’t say How to Polka — for that, you’re in the wrong place. This book is about making beautiful designs using polygons. It’s a practice of formula, calculation and unlimited creativity.
Regan’s primary objective is to show readers new ways to arrange polygons to completely cover surface areas. That’s what “plane tiling” means. While the book explains the technical elements necessary to understand and appreciate the craft, it is clearly and thoughtfully written for designers of any level and aptitude — even if terms like “looping-zigging fractiles,” “zig-zag-zog” and “heptablobs” are foreign to you. And the applications are many: fabric designs, paper cutouts, wallpaper, scarves, hats, or ceramic tiles for floors, walls or walkways.
The joy in Regan’s endeavor is that he sees his work as more than just a process. “You’ll notice right away that, though these patterns are concocted by human hands, they have the kind of beauty only seen in nature,” he writes. “We are discoverers on the plane, rather than inventors.”
You’ll see how polygons fit together on a plane to make attractive, mesmerizing patterns. The book offers detailed instructions and explanations of the underlying concepts and includes many dazzling illustrations of some of the more unusual combinations. Of course, Regan outlines the different combinations of tiling patterns: (1) regular polygons all of one kind; (2) regular mixed; (3) irregular polygons of one kind; (4) irregular mixed; (5) regular and irregular together; (6) concave by themselves; (7) concave mixed; and (8) concave and convex together.
And don’t get caught up in too many colors. Regan cites the “Four-Color Map Theorem,” suggesting that any set of areas on a surface can be colored with only four colors so that no two adjacent areas need be the same color.
While readers may want to explore projects on their own, the images alone are worth the price of admission with many illustrations of the combinations above.
Do I ever think I will want to pursue the art of creating designs using polygons? Maybe as good a chance as learning the polka. But that is hardly a deal-breaker with this title. Whether a professional or hobbyist, there’s a lot to like in this short and succinct volume. One thing to be sure of — if polygon design is a journey you want to take, I can’t imagine a better guide than Regan.
“It is always a delight to see the beautiful symmetries and patterns that arise with polygons,” he says.
