[Feature] Conversions between rhombohedral and hexagonal settings

[janbridley]

Description

Certain rhombohedral unit cells will contain duplicate sets of points, typically in the ratio n_points/n_expected=3, with a few isolated examples of n_p/n_e ∈ {3/2, 7/6}. In the 3x case, the replicated atoms each form a complete, valid unit cell for the crystal with a different translational center but otherwise equivalent spacing: the obverse and reverse settings of the cell. In these cases, we are building a complete hexagonal structure even if the underlying crystal is more simply represented as a rhombohedral one.

Note that this is different from the issue reported in #42 in which numerical precision was the primary driver of duplicate atoms. While this also occurred in a rhombohedral crystal (due to the representation of 1/3 and 2/3 in limited precision), this underlying issue is slightly different.

It is possible to convert to a rhombohedral setting and doing so could aid in particle deduplication. However, it is not trivial to apply periodic boundaries in non-orthorhombic boxes and by changing the cell type we change the fractional coordinates (which can no longer be trivially wrapped).

For now: please let me know if anyone needs the ability to convert between rhombohedral and hexagonal settings. The current construction is unexpected rather than incorrect, so I plan to leave this as is for now.

hR10-SiC:

The non-3x ratios of atoms mentioned above arise from portions of the alternate settings being deduplicated under the standard procedure, resulting in a cell that is no longer equivalent to the original setting.

It is useful to note that this choice is not unique to parsnip - gemmi and ASE show the same behavior with the same structures (+/- about 5 files per thousand that happen to break a uniqueness check).

To reproduce

_space_group_symop_operation_xyz
1 x,y,z
2 -y,x-y,z
3 -x+y,-x,z
4 y,x,-z
5 -x,-x+y,-z
6 x-y,-y,-z
7 -x,-y,-z
8 y,-x+y,-z
9 x-y,x,-z
10 -y,-x,z
11 x,x-y,z
12 -x+y,y,z
13 x+1/3,y+2/3,z+2/3
14 -y+1/3,x-y+2/3,z+2/3
15 -x+y+1/3,-x+2/3,z+2/3
16 y+1/3,x+2/3,-z+2/3
17 -x+1/3,-x+y+2/3,-z+2/3
18 x-y+1/3,-y+2/3,-z+2/3
19 -x+1/3,-y+2/3,-z+2/3
20 y+1/3,-x+y+2/3,-z+2/3
21 x-y+1/3,x+2/3,-z+2/3
22 -y+1/3,-x+2/3,z+2/3
23 x+1/3,x-y+2/3,z+2/3
24 -x+y+1/3,y+2/3,z+2/3
25 x+2/3,y+1/3,z+1/3
26 -y+2/3,x-y+1/3,z+1/3
27 -x+y+2/3,-x+1/3,z+1/3
28 y+2/3,x+1/3,-z+1/3
29 -x+2/3,-x+y+1/3,-z+1/3
30 x-y+2/3,-y+1/3,-z+1/3
31 -x+2/3,-y+1/3,-z+1/3
32 y+2/3,-x+y+1/3,-z+1/3
33 x-y+2/3,x+1/3,-z+1/3
34 -y+2/3,-x+1/3,z+1/3
35 x+2/3,x-y+1/3,z+1/3
36 -x+y+2/3,y+1/3,z+1/3



loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_label
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
K1 K 3  a 0.00000 0.00000 0.00000 1.00000
N1 N 3  b 0.00000 0.00000 0.50000 1.00000
O1 O 18 h 0.13000 0.87000 0.47500 0.50000

>>> CifFile("KNO3_hR8.cif").build_unit_cell().shape
(24, 3) # Should be (8, 3) in the rhombohedral setting