Recently we bought for our small daughter a “Merit” toy, called “Design Doodler” [1], which consists of a single open chain of 8 flat lozenges, linked end to end, identical in size and shape (see Figure 1), the overall length of each being twice the breadth. The linkages are such that the lozenges can move in their own plane so that, when two ends are so linked, any of the five edges of one can be made coincident with any of the five equivalent edges of the other. No other incidence is possible, and lozenges cannot overlap.