Rational approximant structures to decagonal quasicrystals

We have shown earlier that the decagonal quasicrystalline phase can be derived by the twinning of the icosahedral cluster about the five-fold axis by 36°. It is shown here that in a similar fashion, the rational approximant structures (RAS) to the decagonal quasicrystal can be constructed by the twinning of RAS to the icosahedral quasicrystalline phase. The twinning of the Mackay (cubic) type RAS leads to the Taylor (q1/p1, q1/p1) phases, while the twinning of the orthorhombic Little phase leads to the Robinson (q1/p1, q2/p2) approximants to the decagonal quasicrystal. With increasing order of q1/p1 or q2/p2, we approach the digonal quasicrystal with one-dimensional quasiperiodicity.