To figure out how certain crystals work, you have to treat them like they’re 3D slices of a 6D universe.
arXiv · March 17, 2026 · 2603.14590
The Takeaway
Quasicrystals have strange, non-repeating patterns that are impossible to simulate with standard models. By mathematically projecting these structures from six dimensions down to three, researchers found that the material's physical interactions are actually rooted in higher-dimensional space.
From the abstract
Cut-and-project from a symmetric structure in a higher-dimensional space is a standard method for describing the structure of a large class of quasicrystals. By means of a novel localization procedure, we now show how local physical interactions within these quasicrystals are also accurately described by cut-and-project, from corresponding physical interactions in the higher-dimensional space. A density functional theory (DFT++) formulation allows the cut-and-project method to handle the Schroed