The umbilic torus is a single-edged 3-dimensional figure created by Helaman Ferguson as a mathematical artwork. Ferguson created a 27-inch (69 centimeters) bronze sculpture, Umbilic Torus, and it is his most widely known piece of art. The lone edge goes three times around the ring before returning to the starting point. A cross section of the surface taken from an umbilic torus corresponds with a hypocycloid. The torus is defined by the following set of parametric equations.
In 2010, it was announced that Jim Simons had commissioned an Umbilic Torus sculpture to be constructed outside the Math and Physics buildings at Stony Brook University, in proximity to the Simons Center for Geometry and Physics. The torus is made out of cast bronze, and is mounted on a stainless steel column. The total weight of the sculpture is 65 tonnes, and has a height of 28 feet (8.5 m). The torus has a diameter of 24 feet (7.3 m), the same diameter as the granite base. Various mathematical formulas defining the torus are inscribed on the base. Installation was completed in September, 2012.