Three brightly colored tetrahedra, stretched tall, stand erect and in close formation in front of an office building in downtown New Orleans.
Created by local sculptor Arthur Silverman, the artwork is titled Painted Trio. As you walk around it, the sculpture looks startlingly different from different angles, as one sharp edge gives way to another and the sculpture's colored faces—red, green, black, and white—appear in turn.
The tetrahedron is the simplest of all polyhedra—solids bounded by polygons. Any four points in space not all on the same plane mark the corners of four triangles, which serve as the faces of a tetrahedron.
To Silverman, this seemingly humble form is special. "The tetrahedron is very exciting visually," he says. "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 tetrahedron has no right angles, so a tetrahedral structure jars us out of spatial complacency. It has so few faces compared to other polyhedra that its aspect changes abruptly as an observer moves around to view it from different angles.
Silverman has been using tetrahedra as the basic building blocks of his three-dimensional designs for more than two decades. A number of his sculptures are on display in public spaces throughout New Orleans.
Painted Trio is located at 400 Poydras. Silverman's signature piece, dubbed Echo, is a few blocks farther up the street.
To create Echo, Silverman elongated several of a tetrahedron's six edges to create a slim, stainless-steel tower sixty feet high, then twinned it with an identical tower. Standing in the middle of a plaza fountain, this glistening pair seems to soar in formation into the sky.
Arthur Silverman's Echo features a pair of elongated tetrahedra, each balanced on one edge. The sculpture is 60 feet tall and rests on a foundation that extends 20 feet into the ground.
Two more of Silverman's sculptures stand in the grounds around City Hall.
Interlocking Boxes, Closed, is located in front of City Hall in New Orleans.
In this skeletal sculpture near City Hall, Silverman focused on the edges of tetrahedral structures.
"I find that the unique geometric relations intrinsic to the tetrahedron persist in the final sculpture, notwithstanding all the manipulations I carry out," Silverman says.
At the same time, he notes, "photographs do not do these works justice. One must actually see, feel, and walk around these works in order to experience them in their reality."
For more about Silverman's tetrahedral art, see "Art of the Tetrahedron," "Art of the Tetrahedron, Revisited," and "Four Corners, Four Faces."
Peterson, I. 2001. Fragments of Infinity: A Kaleidoscope of Math and Art. Wiley.
Photos by I. Peterson