Fig. 6.

The relationship between mirror symmetries and the number of sides per tile (σ). This image illustrates trigonal, tetragonal and pentagonal tiles in (a) the hexavalent form and (b) as a single tile (along with the 2, 3 and 6-fold symmetry relationships denoted). The dotted lines in the figure indicate possible mirror planes cutting the plane of the paper perpendicularly. It is immediately evident that the hexameric cluster for only σ = 5 has no possible mirror symmetries, which is crucial in the chiral-centric biological world.