Three-dimensional quasicrystalline structures with non-icosahedral global symmetry

The paper discusses a possible atomic structure of a three-dimensional (3D) quasicrystal with the global symmetry that differs from the icosahedral one. The construction of such atomic cluster is performed by expansion of a small initial ‘seed’ using the 1/3 deflation. Here we use a non-icosahedral seed, namely, the Frank–Kasper polyhedron with the coordination number 14. As a result, a 525-atomic cluster is obtained that demonstrates the X-ray diffraction pattern typical rather for quasi-2D quasicrystals. With all atomic positions in the cluster being specified, it is possible to estimate the influence of geometrical restrictions on the possibility of formation of large atomic clusters with such specific symmetry.