# Geographic-style maps for 2-dimensional lattices

arXiv: https://arxiv.org/abs/2109.10885 · HTML: https://mlsanity.com/paper/2109.10885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives](https://mlsanity.com/paper/2303.15385/) (2023)

## Abstract (arXiv)

This paper develops geographic-style maps containing 2D lattices in all known crystals parameterised by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of 2D lattices is a square with identified edges or a sphere without one point. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualise hundreds of thousands of real crystal lattices from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.