Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dedecagonal symmetry. Frank–Kasper, quasicrystalline and related phases in liquid crystals. Stability of quasicrystals composed of soft isotropic particles. Disordered, quasicrystalline and crystalline phases of densely packed tetrahedral. Wave and defect dynamics in nonlinear photonic quasicrystals. Interface-driven formation of a two-dimensional dodecagonal fullerene quasicrystal. Geometry induced sequence of nanoscale Frank–Kasper and quasicrystal mesophases in giant surfactants. Quasicrystallinity expressed in two-dimensional coordination networks. H., Fujita, N., Miyasaka, K., Sakamoto, Y. Quasicrystalline order in self-assembled binary nanoparticle superlattices. Dodecagonal quasicrystalline order in a diblock copolymer melt. Dodecagonal quasicrystalline morphology in a poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) tetrablock terpolymer. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. New type of two-dimensional quasicrystal with twelvefold rotational symmetry. New ordered state between crystalline and amorphous in Ni–Cr particles. Supramolecular dendritic liquid quasicrystals. Quasicrystals and Geometry (Cambridge Univ. The role of aesthetics in pure and applied mathematical research. Concepts, Methods and Structures (Springer-Verlag, 2009). ![]() Metallic phase with long-range orientational order and no translational symmetry. However, our results demonstrate that quasicrystal stability may rest on energy minimization alone, or with only minimal entropic intervention. The stability of random-tiling dodecagonal quasicrystals is often attributed to the entropy of disordering when strict tiling rules are broken, at the sacrifice of the long-range positional order. To maximize the presence of such dodecagonal clusters, the system abandons periodicity but adopts a quasiperiodic structure that follows strict packing rules. The structure consists of dodecagonal clusters made up of triangular, square and trapezoidal cells that are optimal for local packing. Unlike previous dodecagonal quasicrystals based on random tiling, a honeycomb structure based on a strictly quasiperiodic tessellation of tiles is observed. Here, we present a two-dimensional columnar liquid quasicrystal with dodecagonal symmetry. Quasicrystals are intriguing structures that have long-range positional correlations but no periodicity in real space, and typically with rotational symmetries that are ‘forbidden’ in conventional periodic crystals.
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