M. Golubitsky and I. Melbourne

A symmetry classification of columns.

In: Bridges: Mathematical Connections in Art, Music, and Science. (Reza Sarhangi, ed.) 1998 Bridges Conference, 1998, 209-223.

The Yale art historian George Hersey asked us whether the ideas of symmetry breaking could be used to help classify architectural columns. We attempted to answer Hersey in the following way. We view a column as a deformed cylinder and column symmetries as the subgroup of the symmetries of the cylinder that preserve the column.

More precisely, we think of a column as a function on a cylinder (either finite or infinite) where the function tells us how far to deform the cylinder in the direction normal to the cylinder. The symmetries of a column are then the symmetries that preserve the level contours of the function, that is, the isotropy subgroup of the defining function. In this paper we present the mathematical classification of the 29 different types of column symmetry. We note that there is a related classification of the rod groups that corresponds to the columns with discrete symmetry. Level contours (drawn on a flattened cylinder) of representatives of the 28 nontrivial column symmetry types are presented.