cctbx.examples.trigonal_r_vs_tetragonal_i module

The rhombohedral space groups have two commonly used settings, using two different basis systems: “hexagonal basis”, and “rhombohedral basis”. This confused me (rwgk) for the longest time.

The best way to think about this is to compare to, e.g. the tetragonal case, where you have two “Bravais types”, “tetragonal P” and “tetragonal I”. Now, you can transform the tetragonal I groups to a primitive setting. It is still the “tetragonal I Bravais type”, just in a primitive setting, which leads to “weird” unit cell parameters that nobody wants to use.

In the trigonal system you’ll find “trigonal P” and “trigonal R”. As in the case of the tetragonal I, you can convert the trigonal R groups to a primitive setting. However, in contrast to the tetragonal case, you get “nice” unit cell parameters.

See also: http://en.wikipedia.org/wiki/Bravais_lattice

Note that “trigonal P” and “hexagonal P” are the same Bravais type.

cctbx.examples.trigonal_r_vs_tetragonal_i.run(args)