Extended Data Fig. 1: Stacking behaviour of S1 and S2 tiles of DDQC.

(a) Top and side views of a column of S1 tiles. Connecting the centres of only red particles gives triangle tiles and connecting the centres of only green particles gives square tiles of the smallest length scale (S1). (b) Top and side views of a column of inflated (S2) square tiles. Connecting the centres of blue particles give S2 square tiles. Connecting the centres of both blue and yellow particles give S1 square and triangle tiles decomposing the S2 square tiles. The S2 square tile is uniform along the column. The decomposition is not unique and can be alternating along the column as shown in the image. (c) Top and side views of a column of inflated (S2) triangle tiles. The S1 tiles decomposing the S2 triangle tiles show different configurations along the column.