Dodecagonal quasicrystals

There have been few reports to date on quasicrystaUine structure foimatimi from BCPs. Hayashida et al. obtained a 2D quasicrystaUine structure, a tUing pattern with 12-fold symmetry, from an ABC star BCP and homopolymer blend (see Fig. 3) [34]. The Bates group at the University of Minnesota generated a 3D dodecagonal quasicrystal from diblock and tetrablock copolymers [33]. These unique structures are mediated by macromolecular packing frustration. However, a substantial number of unanswered questions about the stmcture formation await further in-depth studies of these interesting morphologies. 

Some stable ternary intermetallic phases have been found that are quasiperi-odic in two dimensions and periodic in the third. These are from the systems Al—Ni—Co, Al—Cu—Co, and Al—Mn—Pd. They contain decagonally packed groups of atoms (local tenfold rotational symmetry). It should be noted that there are also known metastable quasicrystals with local eightfold rotational symmetry (octagonal) and 12-fold rotational symmetry (dodecagonal) as well. The dodecahedron is also one of the five Platonic solids (Lalena and Cleary, 2005). 

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