  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.
