The Geometry of Wigwag and Reversal Linework in Blown Glass

Abstract

Wigwag and reversal linework in blown glass produces periodic wave, spiral, and radiating patterns by twisting longitudinal stripes in alternating directions and then reorganizing the patterned tube. Although glassworkers have developed many consistent techniques and identifiable pattern forms, these patterns do not appear to have been widely described within a common coordinate framework. This paper presents one way of modeling these patterns mathematically. Periodic linework is defined on a cylinder, represented on a sphere, and read relative to a switched axis. The switched pattern may then be re-formed into cylindrical or circular configurations and further manipulated into square, rectangular, or compound forms. The circular case provides a particularly simple radial representation of the switched spherical field. This sequence describes the characteristic organization of a reversal, with the same geometry extending to stacked encalmo sections and other compound structures. The goal is to provide a concise mathematical language for interpreting this broad family of patterned glass forms.