Robust Self‐Similarity and Point Symmetry of Twisted Star‐Like Hinged Grilles

The response to non‐infinitesimal deformations applied at the innermost level of self‐similarity has been studied in star‐like hinged gratings showing a 2D chirality implied by the 2D point group 4 (C 4 ) instead of the achiral point group 4 m (D 4 ) known from previous works. The symmetry lowering turns out to impose geometric restrictions on the existence (feasibility) of such twisted stars as well as on the closeability (full foldability) of their central square orifice. The ranges of feasibility and full foldability have been found as functions of the system's parameters, that is the scaling factor and the twist angle. The minimal angle to which a twisted star can be folded when it is not fully foldable has been determined. For some sets of the parameters, the stars turn out fully rigid, that is not foldable at all if the number of self‐similar generations tends to infinity. When subjected to even large deformations of their central orifice, the twisted stars recover their generic self‐similarity and the four‐fold point symmetry at their periphery but the rate of this recovery depends on the twist angle. The results may be useful in the design of nanometric and macroscopic systems based on metamaterials.