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Pseudo-crystals of the group 14 elements with both 5-fold central rotation symmetry and divisional translation symmetry

Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the fully periodic translation symmetry. Materials containing rotation symmetries forbidden in crystals can be optionally described as quasicrystals with aperiodicity. The theoretical predictions and experimental discoveries of quasicrystals have enriched the knowledge of crystallography and topology, and expanded the capability of growing novel materials. Mathematically, one can fill the whole space with quasi-uniform lattices through divisional translations and arbitrary n-fold central rotations, including the 5-fold symmetry. However, it is unknown if such pseudo-crystals with 5-fold symmetry exist in reality. Here we propose a generalized crystal-prediction-method which can be used to search for potential pseudo-crystals possessing both arbitrary n-fold rotation symmetry and divisional translation symmetry. Successful examples with 5-fold central rotation symmetry based on the group 14 elements are discussed. We expect timely experimental explorations on such peculiar structures, especially on the very promising clathrate phases of the group 14 elements with only slightly larger binding energies compared with the diamond phases.