  The last decade has seen intense research in materials with reduced
dimensionality. The low dimensionality leads to interesting electronic behavior
due to electronic confinement and reduced screening. The investigations have to
a large extent focused on 2D materials both in their bulk form, as individual
layers a few atoms thick, and through stacking of 2D layers into
heterostructures. The identification of low-dimensional compounds is therefore
of key interest. Here, we perform a geometric analysis of material structures,
demonstrating a strong clustering of materials depending on their
dimensionalities. Based on the geometric analysis, we propose a simple scoring
parameter to identify materials of a particular dimension or of mixed
dimensionality. The method identifies spatially connected components of the
materials and gives a measure of the degree of "1D-ness," "2D-ness," etc., for
each component. The scoring parameter is applied to the Inorganic Crystal
Structure Database and the Crystallography Open Database ranking the materials
according to their degree of dimensionality. In the case of 2D materials the
scoring parameter is seen to clearly separate 2D from non-2D materials and the
parameter correlates well with the bonding strength in the layered materials.
About 3000 materials are identified as one-dimensional, while more than 9000
are mixed-dimensionality materials containing a molecular (0D) component. The
charge states of the components in selected highly ranked materials are
investigated using density functional theory and Bader analysis showing that
the spatially separated components have either zero charge, corresponding to
weak interactions, or integer charge, indicating ionic bonding.
