Elizabeth Whiteley

Studio Artist
Washington DC
As a continuation of my explorations in the geometry of pattern design, I am studying line group symmetries.

Textbook examples tend to use friezes to demonstrate the seven line groups. Those examples do not answer a basic question for artists: How do you turn the corner? That is, if you want to create an illustrated rectangular border based on the symmetry of a particular line group, what happens at the vertices?

My research uncovered solutions in a book on tessellations for quilt makers. I applied that guidance to borders on my original drawings. The corners are transitional focal points which indicate a change of axial direction as the viewer’s eye moves horizontally or vertically around the border.
Ginko 1
51 x 41 cm
Silverpoint Drawing on Coated Paper
2015
This original hand-drawn image includes a border which illustrates Group t (sometimes noted as p) from the seven line groups. The generator, or fundamental region, is a 2-leaf motif formed of a diagonal mirror image of a single leaf, within an implied square. The operation is translation of that generator.

A property of the Group t border is that in order to have the corner turn symmetrically, there must be a mirror of the generator at the center of each of the 4 sides. The corners will then match.

My drawing process began by coating the paper with a metalpoint ground based on a Renaissance bone ash formula. I drew with a stylus of sterling silver wire. The rough texture of the ground allowed tiny particles of metal to adhere.