The Symmetry Portfolio by Arthur Loeb

“Space is not a passive vacuum, but has properties that impose powerful constraints on any structure that inhabits it.”
Arthur Loeb, Space Structures, Their Harmony and Counterpoint, 1976

The Arthur Loeb Design Science Teaching Collection at RISD consists of 412 three dimensional structural and tensegrity models including Loeb’s “Moduledra” prototypes, Stewart Coffin puzzles, and Dennis Dreher jitterbugs. The collection includes The Symmetry Portfolio, 164 geometric silkscreens produced by Loeb and his teaching assistant, artist Holly Alderman, that present all infinite tessellating symmetry systems possible in the plane.

Arthur Loeb’s intent for The Symmetry Portfolio was to display all the possible networks of two dimensional structures and to invite students to read between the lines of patterns, to find the inter-connections, roto-centers, symmetry lines, mirrors, glides, reflections, angles, relationships, and repetition of elements. He used them as games and enigmas to pose and answer rhetorical and hypothetical questions during lectures and demonstrations.

Each silkscreen represents one of the limited number of structures that can exist in 2D. Each structure is identified by a code, a sequence of several primary numbers. The code specifies the precise rotocenters, mirror and glide lines of the structure. The codes serve as the titles for the prints and they are all the possible solutions to Euler’s Law, the equation, 1/k + 1/l = 1/m = 1.

At the RISD Nature Lab, the Loeb teaching collection complements other means of exploring pattern, form, and structure at multiple scales by providing students with tangible, “interactable” polyhedral structures and prints that exemplify the infinite arrays, limits, and freedom of modular design found in nature, engineering, and art.