The “football” of the title refers to what people in the US call a “soccer” ball, and it is of course different in both size and shape from an American football and the ball used in rugby. (The translator of the book (written originally in French) makes this clear in an introductory note.) Footballs in this book are approximately round, and this book is mostly about aspects of their geometry.

The starting place is a standard soccer ball called Telstar with a surface covered by black and white panels. The black panels have five sides and there are twelve of them. White panels have six sides, and there twenty of them. The author discusses some of the commonly used patterns (including the Champions League ball that’s uses twelve five pointed stars and twenty white six sided panels.) This leads into an extended discussion of how a ball that is approximately spherical can be covered by regular figures like polygons.

The author provides very good colorful illustrations and they a highlight of the book. He considers how the surface of a ball-like figure could be assembled by gluing together triangles, squares, and pentagons, and notes that hexagons won’t work. The Platonic solids, he notes, are too pointy to make balls, so one just cuts off the points. This eventually leads to the insight that the Telstar ball is a truncated icosahedron. He also explores the evolution of designs of the ball used for the World Cup. The ball used in the Germany in 2006, for example, used panels with polygons having curved sides.

The physics of the movement of soccer balls depends on the weight, drag, and spin of the ball and the roughness of its surface. The author briefly discusses some of the primary elements that influence the dynamics of the ball in flight and their consequences.

A final chapter addresses more geometry: the rigidity of convex polyhedra and some origami, with a consideration of whether curved origami could be used to form an almost spherical shape.

This is a whimsical book, wherein the author manages to entertain while teaching some aspects of geometry as well as a bit of the physics of a ball in flight. The images are the best part.

Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.