In this 2007 photograph, Arthur Silverman stands with one of his tetrahedron-based sculptures. Both bent columns are identical but look quite different from different viewpoints.
Over the years, Silverman manipulated the tetrahedron's familiar shape into a wide variety of forms that were practically unrecognizable as tetrahedra.
Art of the Tetrahedron
Some might consider the tetrahedron a rather humble geometric figure.
Any four points in space that are not all in the same plane mark the corners of four triangles. The triangles in turn are the faces of a tetrahedron. It's the simplest of all polyhedra--solids bounded by polygons.
If each face is an equilateral triangle, the result is a regular tetrahedron, one of the five Platonic solids.
A regular tetrahedron, framed by a cube.
To sculptor Arthur Silverman of New Orleans, however, the tetrahedron is very special. He has been investigating variations of tetrahedral forms for more than 20 years through his sculptures, many of which are displayed in public spaces in New Orleans and other cities from Florida to California.
"The tetrahedron is very exciting visually," Silverman insists. "It's very difficult to anticipate what you are going to see."
We are accustomed to thinking about orientation in space in terms of three perpendicular axes defining left and right, up and down, and forward and backward. A regular tetrahedron has no right angles, so a tetrahedral structure can jar us out of spatial complacency. Moreover, a tetrahedron has so few faces compared to other polyhedra that its aspect changes abruptly as the observer moves to view it from different angles.
Until age 50, Silverman had been a highly successful surgeon, practicing medicine with considerable enthusiasm and skill. Then he encountered an ailing colleague near death, who advised Silverman that if there were anything he really might want to do, then he ought to do it right away, before the chance slips away.
That encounter changed Silverman's life. He returned to interests that had captured his attention and imagination when he was a teenager. He had visited museums to gaze at statues, and had tried his own hand at carving wood. Then, when studying medicine at Tulane University, he had met a sculpture teacher who had invited him to classes and taught him how to see, in the artistic sense.
During these early explorations, Silverman had discovered the wonders of the tetrahedron, the form to which he returned with a passion many years later.
"When I first encountered tetrahedra, I was immediately fascinated by the notion of using these forms as basic building blocks for three-dimensional designs," he recalls.
So, what can you do with (or to) a tetrahedron?
You can elongate a tetrahedron, stretching several edges to a create a slim, stainless-steel tower, 60 feet high, then twin it with an identical tower in a complementary orientation to produce an elegant pair of structures, which seem to soar in formation into the sky. Such a sculpture stands in the middle of a plaza fountain in New Orleans.
Arthur Silverman's Echo features a pair of elongated tetrahedra, each balanced on one edge.
You can join tetrahedra to form a dramatic aluminum cascade.
Or you can stack them in chunks to produce an eerie column.
You can slice tetrahedra. A vast foyer wall in an office building in New Orleans is covered with aluminum tiles based on such a cross section.
The basic elements of this wall relief are sections made through a group of tetrahedra attached to each other. The changing light that plays over the wall in its foyer setting highlights different areas of the relief.
You can divide tetrahedra, then rejoin them in various ways. You can look at what's left when tetrahedra are cut out of a column or from inside a cube. You can stretch a tetrahedron and turn it inside out. You can stand it on edge or balance it on a vertex. The possibilities seem unlimited.
New Wave by Arthur Silverman. Tulane University, New Orleans, Louisiana.
"I find that the unique geometric relations intrinsic to the tetrahedron persist in the final sculpture, notwithstanding all the manipulations I carry out," Silverman notes. At the same time, "photographs do not do these works justice," he contends. "One must actually see, feel, and walk around these works in order to experience them in their totality."
The sculptor fabricates nearly all his pieces in his studio by welding together metal plates. Altogether he has produced more than 300 sculptures based on the tetrahedron, from large-scale outdoor works to diminutive studio models. "When I get an idea, I play with it as long as I can," he admits.
Arthur Silverman's sculpture of this tetrahedral form looks startlingly different from different viewpoints. Changing the sculpture's orientation gives an observer additional views.
This is art that conveys no political, social, or historical message, Silverman remarks. "The sculpture is strictly a visual experience."
One of the more intriguing of Silverman's tetrahedral creations is an ensemble of sculptures he calls Attitudes. The six pieces are spread across a grassy area at the Elysian Fields Sculpture Park in New Orleans.
All the pieces have the same geometry. Each one is made up of two identical tetrahedrons, having faces in the form of tall isosceles triangles that are welded together to form a single object. In the park, each piece has a strikingly different orientation.
Attitudes by Arthur Silverman features the same geometric form positioned in different orientations.
When an observer walks from piece to piece, "it's hard to believe they are all the same structure," Silverman remarks. "Every time you move, you see something different."
To Nat Friedman, a mathematician and sculptor at the State University of New York in Albany, Silverman's creation is an example of a hypersculpture. Its ensemble arrangement represents a way of seeing a three-dimensional form from many different viewpoints at once.
To see every part of a two-dimensional painting in its full glory, you have to step away from it in the third dimension, Friedman says. To see a three-dimensional sculpture in its totality, you need a way to slip into the fourth dimension. Friedman calls this hypothetical process "hyperseeing." A hypersculpture consisting of a set of several related sculptures provides one way to approximate that experience.
Silverman's Attitudes, for instance, presents multiple views of an object from a single viewpoint, because copies of the same object lie in different orientations.
Originally posted Nov. 8, 1999.
See also "Art of the Tetrahedron Revisited," "Three Sentinels," "Four Corners, Four Faces," and "Two Tetrahedra."
Photos by I. Peterson
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