Anna Osler Shepard (1903–1973) was a sociology and anthropology major with a minor in philosophy. After she graduated from the University of Nebraska, she worked as curator of ethnography at the San Diego Museum of Man. Between 1930 and 1965 she studied optical crystallography, chemistry, physics, mathematics, micro chemical spectroscopy at Claremont College, NYU, MIT, Univ. of Kansas, and Univ. of Colorado. Her most lasting work, on “the petrographic analysis of pottery,” was conducted as geologist at the Carnegie Institution in Washington, D.C. 

She brought her unconventional training to bear on one of the first applications of crystallographic ideas to anthropology in The Symmetry of Abstract Design with Special Reference to Ceramic Decoration (1948). She asked,
What, if any, characteristics are common to all decorative art, what features are most subject to change, how are new elements assimilated and decorative ideas evolved, and in what ways do artistic standards vary from time to time.
Anthropologist Dorothy Washburn and mathematician Donald Crowe explain the role of symmetry in Shepard’s analysis in “Symmetries of Culture”:
Shepard presents the seven classes of one-dimensional infinite design, describes how to classify patterns with alternating motifs, and discusses at length situations where symmetries may be irregular. Her discussion of pattern design from different cultures highlights how certain symmetries predominate, and how changes within a culture can be pinpointed by symmetry analysis.

Peter S. Stevens, a working architect at Harvard University, prepared a combination of his own in Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions published with MIT Press in 1980. 

In the preface, he described the problem as a disconnect between the elegant mathematical pattern identification system used by chemists and crystallographers, and the repetitive designs collected in visual sourcebooks for artists and designers. He writes,
This work attempts a synthesIs of the two perspectives. It Is an encyclopedia, a reference handbook, of repetitive designs organized in accord with established crystallographic notions of symmetry and symmetry operations.
We are happy to be joined by Phillip Ording, professor of mathematics at Sarah Lawrence College, who will lead us through this fascinating, if a bit repetitive, material.
Continues in class . . . 
October 23, 2023
The repetition problem

Handbook-of-Regular-Patterns.pdf (Peter S. Stevens)

Philip Ording