Abstract
We explain techniques for creating mathematical chain mail, by which we mean patterns made from identical linked
ring shapes. Most chain mail currently in existence uses circular, or at least planar, rings which are linked in a variety
of ways. By contrast, we show how a small nonplanar “wiggle” in the shapes permits a marvelous variety of woven
patterns. We give formulas general enough to capture every possible periodic chain mail pattern, but admit that the
issue of weaving and self-avoidance of the rings is a decidedly empirical one. We show photographs of 3D-printed
chain mail as well as virtual images, created and rendered in Rhino using the Grasshopper plugin. We mention color
symmetry in chain mail, as well as possibilities for covering surfaces in mail.
