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Danko Arlington Casts Umbilic Torus S.C.





The Dedication Ceremony Link:  Unveiling of “Umbilic Torus” at Simons Center

Danko Arlington, Inc. is honored to have cast a unique piece of huge mathmatical proportions: The Umbilic Torus S.C (Simons Center).

The Umbilic Torus SC was designed by Dr. Helaman Ferguson, PhD – a brilliant mathematician who specializes in stone and bronze sculptures.   Dr. Ferguson was commissioned by philanthropists, Jim and Marilyn Simons, as an outdoor center piece for their newly constructed Simons Center for Geometry and Physics at Sony Brook University located in Long Island, NY.

The piece is based on of a set of parametric equations which create a deltoid –a type of hypocycloid which looks like a triangle with concave sides.  The shape is created by rolling a fixed point on a circle inside another larger circle.   Anyone who had a spiro-graph drawing set most likely made this design without knowing that it is represented in mathematics as:


When the deltoid is revolved 360 degrees around a perpendicular z axis while simultaneously twisting 120 degrees, the result becomes a single edge twisted doughnut-shaped solid named a deltoid torus.  The equations are as follows:



In addition, to the infinite edge that the shape develops on the torus, this sculpture surface contains another complex equation called a 3-adic curve.  The 3-adic lines are akin to ancient Greek or Mayan  perpendicular-lined patterns which when wrapped around the torus, have no end and no beginning.

The Umbilic Torus SC was cast entirely out of silicon bronze at Danko Arlington welded together as an assembly at the neighboring New Arts Foundry.  The artwork consists of one hundred and forty four individually sand cast sections to create the hollow torus shape, an internal inverted sand cast cap for mounting, and six internal cast buttresses for additional support.  The entire assembly rests on a  custom fabricated stainless steel post and is surrounded by a base consisting of nine slabs of Lake Superior granite in the shape of circle and deltoid section and engraved with the equations.   The total weight of the sculpture is approximately sixty five tons.

This casting of the year candidate is truly unique – not only due to its size and shape, but for the ingenuity used in its creation and design.

Remarkably, the entire torus was cast without pattern tooling.  Each unique twisted panel with associated 3-adic surface curve was individually 5-axis CNC machined into a twenty four hundred pound no bake sand drag.  Thousands of tool path movements moved a rotating diamond-head cutter to accurately make the cavity for each section.  Each drag, known to the art team as ‘sand stone,’ was then hand-clayed for the it approximate 3/8” wall thickness to make its matching cope, then hand cut with risering and gating, assembled, and poured in C87300 silicon bronze (Everdur) at Danko Arlington.   The torus assembly itself is weighs over twenty thousand pounds.

The large bronze cap casting inside the sculpture was produced from a traditionally made hardwood pattern with a machined foam core box.    Each buttress stiffener was cast from a hand-fitted polystyrene pattern to ensure its proper fitting.

Nine cast panel pieces were carefully straightened and welded by the skilled craftsmen at New Arts Foundry and individual 22.5 degree bulkhead sections which were assembled together on top of each other piece by piece – similar to shipbuilding.   Eight bulkheads were welded together to produce a half torus for transport to the University before final, permanent assembly on site.   Countless hours were spent to weld each section joint and each 3-adic curve which was later textured to match the as-cast surface.  The silicon bronze was finished in a light green verde patina which will take on its own color as it weathers.

The project took over two years to construct which included casting two smaller torus casting assemblies of one tenth scale and quarter scale.  Countless hours of collaboration were also spent between Dr. Ferguson and his team of foundrymen, architects, planners, structural engineers, stone masons, and representatives from the University and the Simons Foundation.

The Umbilic Torus SC was dedicated on Thursday, October 25, 2012.  Undoubtedly, this sand cast sculpture will be gazed upon by future generation of students for centuries.   Many will be inspired as the work epitomizes the life-time achievement of two great American mathematicians:  an innovative sculptor as well as a successful businessman and philanthropist, who by the way, named the company where he made his fortune, ‘’Renaissance Technologies.’’

For the team that constructed the Umbilic Torus SC, the implications a project benefactor who values the combination of the words ‘’renaissance” and ”technologies’’ is no mere coincidence.

For as in centuries ago, after years of the Dark Ages, the Renaissance inspired wealthy patrons like the Medici family of Florence to commission new ideas in art, science, and technology.  Lorenzo Ghiberti, Philippo Brunelleschi, Leonardo da Vinci, and Michelangelo Buonarrati are just a few famous names that immidiately come to mind.   Today, we would use the slang term of “thinking outside of the box” to best summarizes their kind of creativity.

So too, therefore, does the design and fabrication of this infinitely curved cast artwork symbolize a new way of thinking for the future of the North American foundry industry,  which makes the Umbilic Torus SC — a true “Modern Casting!“

JDD October 26, 2012