Tessellations

Robert Fathauer has had a life-long interest in art but studied physics and mathematics in college, going on to earn a PhD from Cornell University in electrical engineering. For several years he was a researcher at the Jet Propulsion Laboratory in Pasadena, California. Long a fan of M.C. Escher, he began designing his own tessellations with lifelike motifs in the late 1980s. In 1993, he founded a business, Tessellations, to produce puzzles based on his designs. Over time, Tessellations has grown to include mathematics manipulatives, polyhedral dice, and books. Dr. Fathauer’s mathematical art has always been coupled with recreational math explorations. These include Escheresque tessellations, fractal tilings, and iterated knots. After many years of creating two-dimensional art, he has recently been building ceramic sculptures inspired by both mathematics and biological forms. Another interest of his is photographing mathematics in natural and synthetic objects, particularly tessellations. In addition to creating mathematical art, he’s strongly committed to promoting it through group exhibitions at both the Bridges Conference and the Joint Mathematics Meetings.

1. Introduction to Tessellations. 2. Geometric Tessellations. 3. Symmetry and Transformations in Tessellations. 4. Tessellations in Nature. 5. Decorative and Utilitarian Tessellations. 6. Polyforms and Reptiles. 7. Rosettes and Spirals. 8. Matching Rules, Aperiodic Tiles, and Substitution Tilings. 9. Fractal Tiles and Fractal Tilings. 10. Non-Euclidean Tessellations. 11. Tips on Designing and Drawing Escheresque Tessellations. 12. Special Techniques to Solve Design Problems. 13. Escheresque Tessellations Based on Squares. 14. Escheresque Tessellations Based on Isosceles Right Triangle and Kite-Shaped Tiles. 15. Escheresque Tessellations Based on Equilateral Triangle Tiles. 16. Escheresque Tessellations Based on 60°–120° Rhombus Tiles. 17. Escheresque Tessellations Based on Hexagonal Tiles. 18. Decorating Tiles to Create Knots and Other Designs. 19. Tessellation Metamorphoses and Dissections. 20. Introduction to Polyhedra. 21. Adapting Plane Tessellations to Polyhedra. 22. Tessellating the Platonic Solids. 23. Tessellating the Archimedean Solids. 24. Tessellating Other Polyhedra. 25. Tessellating Other Surfaces.