said. It is represented in mathematics as:
When the deltoid is revolved 360 degrees around a per- pendicular Z axis while simultaneously twisting 120 degrees, the result becomes a single edge twisted doughnut-shaped solid called a deltoid torus. Te equations are as follows:
A bronze cap casting for mounting was produced using a tradition- ally made hardwood pattern with a machined foam corebox.
“Te 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,” Danko explained.
Obstacles Overcome
Initially, the team encountered a challenge when cutting the molds. Hand ramming each sand block created inconsis- tencies in its density. “Areas that were too compact placed more stress on the
In addition to the infinite edge the shape develops on
the torus, this sculpture surface contains another complex equation called a 3-adic curve.
cutter, which created more heat and friction on the tool. Tis caused the system to overload and often shut down,” said Danko. Experimentation and feedback resulted in improved hand ramming and more uniform density blocks for the process, so the movements flowed more uniformly. Te sand was vacuumed by hand. Each drag, known to Ferguson’s art
team as a “sand stone,” was then hand clayed following each 3-adic curve for the approximate 3/8-inch wall thick- ness to make its matching cope. “In this way, the need for a
machined sand cope was eliminated, saving time, cost and logistics,” said Danko. “[Each] cope was molded right on top of each custom drag mold.” Te clay was removed and the drag was hand cut for risering and gating. Once assembled, Danko Arlington
Eight bulkheads were welded together to produce a half torus for transport to final assembly onsite.
36 | METAL CASTING DESIGN & PURCHASING | May/Jun 2013
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