Robert Fathauer

Small business owner, puzzle designer, author, and artist
Tessellations Company
Phoenix, Arizona, USA
Mathematical structure is evident throughout the natural world. My work explores the mathematics of symmetry, fractals, tessellations and more, blending it with plant and animal forms as well as inorganic forms found in nature. This synthesis allows me to create innovative prints and sculptures that derive their beauty from a combination of complexity and underlying order.
Five-fold Ringworm
8" x 14" x 14"
This negative-curvature surface is based on forms seen in polyclad flatworms. These sea creatures are not ring shaped, but this sculpture is an imagining of a five-fold ring of such curved surfaces. This object also has two-fold symmetry axes orthogonal to the five-fold axis and mirror planes that contain the five-fold axis. The piece belongs to the spherical symmetry group 2*5.
Flatworm Form No. 3
5" x 11" x 9"
This negative-curvature surface is an inspired by the shapes polyclad flatworms take on in open water. It can also be thought of as a piece of a hyperbolic plane embedded in Euclidean 3-space.