Five Elements: Lake Superior, Eagle River, 2011, optical glass, black and white film, 6" x 3" x 3" (15.2 cm x 7.6 cm x 7.6 cm), © Hirsohi Sugimoto, courtesy The Pace Gallery, Photo courtesy the artist and The Pace Gallery.

Hiroshi Sugimoto’s “Surface of the Third Order” is currently on view through December 23, 2011 at The Pace Gallery, 510 West 25th Street. The exhibit is comprised of two different collections of three-dimensional art, both aluminum sculpture and five-element crystal pagodas. Even though the two sets are dramatically opposed in material and size, they are united by mathematical concepts of geometry and infinity.

The viewer begins in the first room with four aligned aluminum poles shaped by mathematical models. Simple and rhythmic, the sculptures are placed on a mirrored base to show a continuity and elongation of shape. The conceptual models show the sharpness and precision of metalwork and the simultaneous softness of these patterns that appear in nature. Of the aluminum sculptures, Conceptual Form 009 manifests these ideals most strikingly. Using the equation of a surface that contains a single point extending to infinity, Sugimoto has created a cone-like shape out of metal that deceptively appears to be stretched to a point, with a one-millimeter diameter, so much so that the aluminum seems to evaporate. This incredible extension above the viewer is then reflected on the mirror placed beneath the base of the structure. Sugimoto has effectively created aluminum infinity.

In the second body of work on the other side of the dividing wall, Sugimoto has created ten crystal pagodas that are much smaller than the aluminum sculptures yet display the same meticulousness. Each geometric pagoda is made of five representations of the elements earth, water, fire, wind and emptiness. The sculptures are made of optical-quality glass, and tucked within each spherical section of the pagoda is a black and white photograph from Sugimoto’s “Seascape” series. The crystal of the pagodas works to amplify the “Seascape” images and achieve another concept of infinity within the earthly realm.

Five Elements: Bay of Sagami, Atami, 2011, optical glass, black and white film, 6" x 3" x 3" (15.2 cm x 7.6 cm x 7.6 cm), © Hiroshi Sugimoto, courtesy The Pace Gallery, Photo courtesy the artist and The Pace Gallery.

Mathematical Model 010 Onduloid: a surface of revolution with constant non-zero mean curvature aluminum, iron, 2007, aluminum and iron, Total height: 14' 9-13/16" (451.7 cm) model height: 14' 3-15/16" (436.7 cm); base: 19-11/16" x 5-7/8" (50 cm x 15 cm), © Hiroshi Sugimoto, courtesy The Pace Gallery, Photo courtesy the artist and The Pace Gallery.

Mathematical Model 002 Dini's surface: a surface of constant negative curvature obtained by twisting a pseudosphere, 2005, aluminum and iron, Total height: 109-1/2" (278.2 cm); model height: 103-1/4" (262.2 cm), base: 9-13/16" x 3-1/8" (25 cm x 8 cm) and 7-7/8" x 3-1/8" (20 cm x 8 cm), © Hiroshi Sugimoto, courtesy The Pace Gallery, Photo courtesy the artist and The Pace Gallery.