Abstract
Bobbin lace is a 500-year-old ber art form created by braiding together ne threads. In its design, lacemakers
employ doubly periodic textures to create contrast and interest in a predominantly monochromatic fabric. In the past
we have created a model for these doubly periodic patterns which employs graph drawings to describe the ow of
threads. In this paper we demonstrate that these graph drawings, which we call `tesselace patterns', exist for each
of the 17 planar periodic symmetry groups. We provide an algorithm for exhaustively generating patterns with a
particular symmetry on a grid of xed size. We also explore the symmetry of the interlaced fabric resulting from
these patterns.
