# Fundamental Frieze Scroll I

Merino/alpaca yarn, glass beads

2018

Joint Mathematics Meeting Exhibition of Mathematical Art, Baltimore, January 2019

*The Fundamental Frieze Scroll* series follows in the footsteps of earlier pendants depicting the seven frieze groups in knitted lace. In those works, each of the seven designs occupies the same amount of space, regardless of complexity. Here, each frieze design is generated by the same fundamental region, a rectangular pattern with no internal symmetries that is rotated, reflected and/or translated to make the full pattern. Each design uses only enough copies of this rectangle to generate three translations of its primitive cell, the smallest region that can produce the whole design through translational symmetries.

Glass beads incorporated during the hand-knitting process highlight the symmetries in the Fundamental Frieze Scroll series. White beads mark reflection axes, yellow beads mark glide reflection axes, and blue beads mark centers of rotation. The red beads along the edges of the designs mark their translational symmetries, with the minimal duplication needed to preserve reflections, glide reflections and rotations.

In *Fundamental Frieze Scroll I*, the fundamental region design is a lace rendition of a Truchet tile, a rectangle divided along a diagonal into light and dark triangles. Truchet tiles appear in many recent mathematical artworks, including Carolyn Yackel's lace knitting.