Polyhedra Primer

Peter Pearce is an American product designer, author, and inventor. He was an assistant to Buckminster Fuller. Like his mentor, Pearce looks for inspiration from basic two- and three-dimensional polytopes. This primer is a catalog of images and descriptions with only rudimentary mathematics, such as a statement of Euler’s formula relating the number of vertices, edges and faces of a convex polyhedron. First published in 1978, it is a visual gallery of inspiration for designers, architects, artists, and other creators.

Two chapters of planar explorations featuring polygons and tessellations lead off the seven chapters. This includes dual tessellations, which appear to me as plane-filling inspiration for stained glass motifs.

The book is largely a simple dictionary; to call it an encyclopedia would be suggesting too much. For instance, the 15-sided pentadecahedron (here, pentakaidecahedron) is noted to have “15 faces”. There are numerous topologically distinct forms of a pentadecahedron and two wireframe examples accompany the single-sentence definition. This is not meant to be an exhaustive collection of polyhedra, which cannot be practically cataloged. Rather, it is an atlas of geometric possibilities.

Sculptural or structural possibilities are suggested by the space-filling and open packing chapters. A final chapter on constructions starts back in the plane with bisections, regular polygons, and more. It also includes tape, cardboard, and razor techniques for bringing to life many polyhedra.

Tom Schulte teaches algebra to students at Oakland Community College and hopes Pearce will produce a similar edition with quadratic surfaces. If not, he may produce his own.