This tool takes in **input a crystal structure** (in a number of different formats), and

- finds its
**spacegroup**; - computes the
**crystallographic primitive cell**(i.e., always oriented according to crystallographic standard definitions); - computes the
**Brillouin zone**; - provides
**interactive visualization**of primitive cell and Brillouin zone; - computes all
**high-symmetry k-points coordinates**; - for band structure plotting, provides a
**complete list of high-symmetry paths**in the Brillouin zone going between the high-symmetry k-points; - provides
**copy-paste content**to input the kpoints in an external code or input file.

*Alternatively, you can calculate and visualize an example*.

(There is one example for each possible extended Bravais symbol, both for systems with and without inversion symmetry.)

This tool follows the definitions of the HPKOT paper. The main advantages of this work are:

**use of the**: The conventional cell is standardized according to the definitions that are standard in the field in crystallography: the*crystallographic*cells*International Tables of Crystallography*(the Tables, from here on), and*Parthé, Gelato, Acta Cryst. A40, 169 (1984)*. Just a couple of examples:- orientation of the axes follows the standards mentioned above, e.g., monoclinic cells are always
*b*-axis unique. - order of axes is imposed only when not already imposed by symmetry, (following the prescriptions of Parthé and Gelato). E.g., for spacegroup Pmm2 (orthorhombic), the third axis is fixed by symmetry (the one with 180° rotation but no mirror plane). Therefore, we only impose
*a<b*, with no ordering imposed on*c*.

- orientation of the axes follows the standards mentioned above, e.g., monoclinic cells are always
**Unambiguous high-symmetry k-point labels**. For rational k-points, we use the same labels as the ones defined in the Tables. For irrational k-points (not defined in the Tables), letters are chosen so as to never collide with existing letters in the Tables.**Complete set of high-symmetry paths (band lines), using also spacegroup symmetry when needed**. For instance, spacegroup Pm-3 (cubic primitive, extended Bravais lattice cP1) does not have 90° rotation symmetries, so both the lines M–X and M–X_{1}must be considered.

If you use this tool, please cite the following work:

- Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, I. Tanaka, Band structure diagram paths based on crystallography, Comp. Mat. Sci. 128, 140 (2017). DOI: 10.1016/j.commatsci.2016.10.015 (the "HPKOT" paper; arXiv version: arXiv:1602.06402).
- You should also cite Spglib that is an essential library used in the implementation: A. Togo, I. Tanaka, "Spglib: a software library for crystal symmetry search", arXiv:1808.01590 (2018)
- The input parsers use a number of libraries (see name in the dropdown list) from ASE, qe-tools or pymatgen.

Note: if you want to use the code on your computer, you can download the SeeK-path python library from the SeeK-path GitHub repository.