We have shown earlier that the decagonal quasicrystalline phase can be deri
ved by the twinning of the icosahedral cluster about the five-fold axis by
36 degrees. It is shown here that in a similar fashion, the rational approx
imant 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 o
rder of q1/p1 or q2/p2, wt approach the digonal quasicrystal with one-dimen
sional quasiperiodicity. (C) 2001 Published by Elsevier Science B.V.