Helicity in solids often arises from the precise ordering of cooperative intra- and intermolecular interactions unique to natural, organic or molecular systems. This exclusivity limited the realization of helicity and its ensuing properties in dense inorganic solids. Here we report that Ga atoms in GaSeI, a representative III–VI–VII one-dimensional (1D) van der Waals crystal, manifest the rare Boerdijk–Coxeter helix motif. This motif is a non-repeating geometric pattern characterized by 1D face-sharing tetrahedra whose adjacent vertices are rotated by an irrational angle. Using InSeI and GaSeI, we show that the modularity of 1D van der Waals lattices accommodates the systematic twisting of a periodic tetrahelix with a 4₁ screw axis in InSeI to an infinitely extending Boerdijk–Coxeter helix in GaSeI. GaSeI crystals are non-centrosymmetric, optically active and exfoliable to a single chain. These results present a materials platform towards understanding the origin and physical manifestation of aperiodic helicity in low-dimensional solids.

固体中的螺旋性通常源于自然、有机或分子系统特有的分子内和分子间合作相互作用的精确排序。这种排他性限制了螺旋性的实现及其在致密无机固体中的随之而来的特性。在这里，我们报道了 GaSeI（一种代表性的 III-VI-VII 一维（1D）范德华晶体）中的 Ga 原子表现出罕见的 Boerdijk-Coxeter 螺旋图案。该图案是一种非重复的几何图案，其特征是一维共面四面体，其相邻顶点旋转无理角度。使用 InSeI 和 GaSeI，我们表明一维范德华晶格的模块化可以适应 InSeI 中具有 4 ₁螺旋轴的周期性四螺旋到 GaSeI 中无限延伸的 Boerdijk-Coxeter 螺旋的系统扭曲。 GaSeI 晶体具有非中心对称性、光学活性并且可剥离成单链。这些结果为理解低维固体中非周期螺旋性的起源和物理表现提供了一个材料平台。