Chiral spiral cyclic twins

A formula is presented for the generation of chiral m-fold multiply twinned twodimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.

Automated summary

A formula is presented in this paper for generating chiral m-fold multiply twinned two-dimensional point sets with even twin modulus m > 6 from an integer inclination sequence. It particularly discusses the first three non-degenerate cases m = 8, 10, 12, which are connected to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal, and dodecagonal long-range orientational order and symmetry.