Strip Symmetry Groups of African Sona Designs

The sona drawings of the Chokwe people of Angola/Congo are continuous one-line drawings, generally made in the sand, that are often used to build highly symmetric one-line drawings. A large class of these drawings can be viewed as a form of “mirror curves,” visualizable as a curve bouncing through an arrangement of dots, bouncing off “mirrors” placed between some of the dots, and leaving a symmetric, closed trail behind. To investigate some of the possibilities for such Chokwe sona, we construct such sona for all 7 strip symmetry groups on all but the smallest rectangles. This allows us to use mathematical techniques to build classes of sona that, we argue, meet the artistic goals of the Chokwe people, and (we hope) would be viewed favorably by the historic artists of this culture.