Hidden in Plain Sight: Overlooked Polyhedral Shapes and Metal-Centered Chirality in Lanthanide Coordination Complexes

For an sp³ carbon atom, chirality is part of the textbook language of chemistry. For high-coordination environments typical of lanthanide ions, however, no comparable stereochemical formalism is routinely employed and, consequently, two structural features often pass unnoticed. The first is the coordination polyhedron itself: geometries outside the canonical set are frequently described as severely distorted octahedra or prisms, even when this conceals actual symmetry. The second is chirality at the metal center, a property that may be present but is seldom recognized, although it can affect molecular recognition, chiroptical response, and crystal packing. In this presentation, we combine Pólya's enumeration theorem, Steinitz's theorem, and graph theory with Cambridge Structural Database entries, in order to ask how many shapes a coordination number actually demands, whether an unnamed coordination polyhedron may outnumber a familiar one, and how often metal-centered chirality remains hidden in achiral reports. The answers are more surprising than expected.