## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## April 1, 2007

### Four Corners, Four Faces

To Arthur Silverman, a sculptor in New Orleans, tetrahedrons, or triangular pyramids, are very special. He's been creating sculptures based on the tetrahedron for more than 20 years. You might see examples on display in plazas and office buildings in New Orleans, San Francisco, and other cities in the United States.

Until the age of 50, Silverman had been a successful surgeon. He gave that up, however, to return to interests that had captured his attention when he was a teenager and had visited art museums and tried carving wood.

To make a tetrahedron (above), imagine four points in space. If you join all of the points, the points become the corners of four triangles. The four triangles form the faces of a tetrahedron.

"The tetrahedron is very exciting visually," Silverman says. "It's difficult to anticipate what you are going to see." For example you can stretch several edges of a tetrahedron to create a slim, tall tower. Silverman has a pair of such towers, each 60 feet high, in the middle of a plaza fountain in New Orleans.

The Energy Centre fountain in New Orleans, a sculpture by Arthur Silverman, is made of two tetrahedrons.

You can join tetrahedrons together to create an angular wall down which water can tumble and fall. You can stack them in various ways to create a monument. Or you can balance then on edge or on a corner.

You can also slice tetrahedrons to get interesting cross sections, which can then be used as tiles to cover a wall. You can divide tetrahedrons into intriguing pieces, and then rejoin them in various ways. The possibilities seem endless.

If each face of a tetrahedron is an equilateral triangle, the result is a regular tetrahedron, one of the five Platonic solids. Here, a tetrahedron is shown inside a cube, another Platonic solid.

Silverman has produced more than 300 sculptures based on the tetrahedron. "When I get an idea, I play with it as long as I can," he notes.
Sometimes it takes an artist to reveal the many wonders of a seemingly simple geometric form like the humble tetrahedron.

Muse, April 2000, p. 26.