An error occurred in Philosophical Magazine, Volume 88, Issus 13–15, 1–21 May 2008, pp. 1905–1912, in the article ‘Geometrical property of the cluster model of the Yb–Cd icosahedral quasicrystal’.
The first paragraph on page 1911, reads:
1/1 cubic approximant crystals of Yb–Cd type have unique cluster configuration of (14, 6, 8). Their space filling structures can be described by only RT clusters [7]. 2/1 cubic approximant crystals also have unique configuration of (13, 6, 7), but for their space filling structures one AR per unit cell is necessary besides RT clusters [6]. If one considers a fictitious 3/2 cubic approximant crystal with space group Pa 3, which can be derived from the present Yb–Cd i-QC model together with the above 1/1 and 2/1 approximants, nine ARs per unit cell are necessary besides RT clusters for its space-filling structure [16].
The underlined elements in the above paragraph are incorrect. The correct paragraph should read:
1/1 cubic approximant crystals of Yb–Cd type have unique cluster configuration of (14, 6, 8). Their space filling structures can be described by only RT clusters [7]. 2/1 cubic approximant crystals also have unique configuration of (13, 6, 7), but for their space filling structures four ARs per unit cell are necessary besides RT clusters [6]. If one considers a fictitious 3/2 cubic approximant crystal with space group Pa 3, which can be derived from the present Yb–Cd i-QC model together with the above 1/1 and 2/1 approximants, 36 ARs per unit cell are necessary besides RT clusters for its space-filling structure [16].
The authors would like to apologise for this mistake.