Crystallographic Coordinates & Symmetry

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Abstractions about fractional coordinates, low-discrepancy sequences, line and rod symmetry groups, and mappings of material structure.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Fractional coordinates — Crystal coordinates expressing a point as coefficients of the unit-cell lattice basis.
• Halton sequence — A deterministic low-discrepancy sequence in the unit cube formed by combining one-dimensional radical-inverse sequences in pairwise coprime bases.
• Line group — A discrete symmetry group of a structure periodic along one spatial axis, combining axial translations or screw operations with compatible point symmetries.
• Rod group — One of the three-dimensional crystallographic line groups describing structures periodic along exactly one spatial direction.
• Structure Field Map — An empirical materials map that places compositionally comparable crystalline compounds in descriptor coordinates and uses the resulting structure-type fields as an interpretable classification and candidate-structure prior.