It's all in the group

The Cayley graph of a crystallographic group, although depending only on intrinsic information from the group, often allows the derivation of interesting combinatorial and geometric properties of crystal structures on which the group acts [Baburin (2026). Acta Cryst. A82, 18–31].

Quasicrystals from the edge: extreme environments, impact craters and the quest in other celestial bodies

Natural quasicrystals from the Khatyrka meteorite reveal that hypervelocity impacts can generate and preserve quasiperiodic phases under extreme non-equilibrium conditions. Their occurrence highlights the role of quasicrystals as robust markers of shock processes, offering new insights into the collisional and chemical evolution of planetary bodies.

Exploring oxide quasicrystals in internal space

The internal space expansion with variable system size is investigated for three different oxide quasicrystal systems. Patches of 7800, 4800 and 3600 vertices are examined in Ba–Ti–O/Pt(111), Eu–Ti–O/Pd(111) and Sr–Ti–O/Pd(111), respectively. This internal space inspection provides unique structural information for quasicrystalline systems, which goes far beyond a tiling analysis in the physical space.

Minimal-transitivity finite tangles and catenated polyhedra

We enumerate and describe piecewise-linear embeddings of cubic and icosahedral tangles and linked polyhedra with one kind of vertex and two kinds of edge.

Structural investigation and C₆₀ adsorption on the (100) surface of a 1/1 pseudo-Tsai-type Au–Si–Ho quasicrystalline approximant

The decoration of cluster centers, while not modifying the surface plane selection rule established for Tsai-type quasicrystals and approximants, affects the superstructure type stabilized at the surface.

Primitive icosahedral quasicrystals in ZnMgLi(Dy, Ho, Er, Tm) systems

The study introduces new primitive icosahedral quasicrystals in Zn–Mg–Li–(Dy, Ho, Er, Tm) systems. Quasicrystals are studied with an X-ray diffraction technique resolving the local atomic structure.

Symmetry structures of tilings on a Klein bottle

This study presents a comprehensive characterization of the symmetry structures of tilings on a Klein bottle, arising from tilings of the Euclidean plane with crystallographic symmetry groups containing a subgroup of type pg.

P³, linearizing unit-cell parameters

P³ is a linearized description of unit-cell parameters, created from the usual lengths and angles of the unit cell. It provides a useful metric for comparing unit cells and a convenient base for displaying and comparing unit cells.

Approximate lattice matching in three dimensions

A solution is proposed for the problem of best matching the lattices of unit cells that are described in different presentations along with the three-dimensional matrix that defines the relationship between matched lattices.

International Tables for Crystallography, Volume I, X-ray absorption spectroscopy and related techniques