Vitaliy Kurlin's talk at the MIF++ seminar on 28th January 2022, https://kurlin.org/MIFplusplus.php
Channel: Vitaliy Kurlin
Date: 2023-11-09

Title. Geographic-style maps of crystal lattices.
Abstract. The Crystal Isometry Principle (first presented at MACSMIN 2021, http://kurlin.org/macsmin.php#2021) says that all real non-equivalent crystals should be geometrically recognizable by their periodic structures of atomic centres without any chemical data. As a consequence, all known and not yet discovered periodic crystals live in a common Crystal Isometry Space (CRISP), similar to all chemical elements in Mendeleev's table. The space CRISP can be continuously and unambiguously parameterised by complete isometry invariants, which found unexpected duplicates in the Cambridge Structural Database (CSD), now under investigation by five journals. The talk will present visual maps of CRISP for hundreds of thousands of crystal lattices from the CSD. These maps support the natural preference for higher symmetry crystals and experimentally justify the continuity of CRISP. The latest versions of the underlying papers are linked at the Periodic Geometry page, http://kurlin.org/projects/periodic-geometry-topology.php.