The umbilic torus is a single-edged 3-dimensional figure created by Helaman Ferguson

Helaman Ferguson

Helaman Rolfe Pratt Ferguson is an American sculptor and a digital artist, specifically an algorist.Ferguson's mother died when he was about three and his father went off to serve in the Second World War. He was adopted and raised in New York. He was a graduate of Hamilton College and received a...

 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

Cross section (geometry)

In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

 of the surface taken from an umbilic torus corresponds with a hypocycloid

Hypocycloid

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle...

. The torus is defined by the following set of parametric equations.

In 2010, it was announced that Jim Simons

James Harris Simons

James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over $15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...

 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

Simons Center for Geometry and Physics

The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2007 by a gift from the James and Marilyn Simons...

. The torus will be made out of cast bronze, and will be mounted on a stainless steel column. The total weight of the sculpture will be 65 tonnes, and will have a height of 28 feet (8.5 m). The torus will have a diameter of 24 feet (7.3 m), the same diameter as the granite base. Various mathematical equations will be inscribed on the base. Installation should be complete by Summer of 2011.