ABSTRACT
This chapter enumerates the plane symmetry groups which may be classed according to their translational structure. It discusses three cases: no translations present, the two finite point groups; one translation present only, the seven frieze groups; and more than one direction of translation, the seventeen wallpaper groups. Claude-Nicolas Ledoux and Sir John Soane at the end of the eighteenth century made interesting use of the dihedral group in their works. The need to repeat functional elements to justify the threefold symmetry appears absurd, and such buildings are rarely, if ever, built. In St Mark’s Tower, Wright effectively takes a rectangular ‘corner’ of the triangular grid – one edge coinciding with an axis of the tesselation, the other at right angles bisecting a row of equilateral triangles.
