Periodic Platonic solids: the royal family of periodic nets

Analogous to the Platonic solids, Li et al. [Acta Cryst. (2025), A81, 419–426] identify a rare class of `supersymmetric' periodic nets that occupy the extreme limits of symmetry in Euclidean space. This commentary discusses how these structures provide a rigorous geometric toolkit for engineering advanced properties in systems ranging from molecular frameworks to macroscopic lattices.

Geometric indicators of local plasticity in glasses measured by scanning small-beam diffraction

Deformation defects in structurally disordered glasses are much more difficult to detect and characterize than defects in crystals. Here we show how well defined geometric indicators of local plasticity in glasses can be measured using scanning small-beam diffraction.

Short presentations for crystallographic groups

A practical approach is proposed for constructing short presentations for Euclidean crystallographic groups on given generating sets.

On artificial crystal structure generation for solving the phase problem with deep learning

A new approach for generating training data for solving the phase problem with deep learning is proposed. Models trained on such data are better at generalizing the solution for structures outside the training domain.

An extensible Julia toolkit for symmetry-aware dual-space phasing in arbitrary dimensions

A Julia toolkit for dual-space phasing in arbitrary dimensions is presented. It offers a flexible platform for developing and testing charge-flipping algorithms under symmetry constraints.

Enhanced X-ray structural analysis using total variation denoising of X-ray diffraction images

Denoised X-ray diffraction images by total variation regularization were used to improve the accuracy of X-ray structure analysis of a small-molecule crystal.

A new order parameter model for the structural phase transitions in VO₂-based solid solutions

To describe the structural phase transitions P4₂/mnm(R) ↔ P2₁/c(M₁) ↔ P1(T) ↔ C2/m(M₂) observed experimentally in VO₂ and its solid solutions, the two-component order parameter model is newly proposed.

On colourings of cubic lattices – a tribute to Heinrich Heesch

For cubic lattices Λ^d in dimensions d ≤ 4, partitions of the lattice nodes into orbits of finite-index subgroups of Aut(Λ^d) have been computed. Complete results are obtained for d = 2 up to 64 orbits, for d = 3 up to eight orbits, and for two orbits in dimension 4.

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