Spgroup 151 not respecting Wyckoff multiplicity

Dear community, (edit below)

I would like to simulate a material belonging to space group 151. I have noticed that, when I use the spgroup variable to generate the atomic positions from the symmetry-inequivalent atoms, an atom in a position 3a according to
https://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-wp-list?what=wpos&gnum=151
generates 6 different atomic positions as opposed to the expected 3. I am running v9.6.2.

This can be reproduced with the following minimal example, adapted from tests/v4/Input/t28.abi

# Fake H crystal.
# Test trigonal and hexagonal spacegroups

spgroup 151
natom 6

#This is for hP Bravais lattice
acell     2*10. 30.    angdeg    2*90. 120.

# Common data
prtvol -1          # stop in abinit (main program), before call driver.
brvltt -1          # important to reduce the conventional cell to primitive,
                   # and allow the recognition of space group
ntypat 1
znucl 1
natrd 1
xred 0.15   0.30  0.666666666666667
typat 1
ecut 1
kptopt 0   nkpt 1
nline 1    nstep 1
toldfe 1.0d-6

pp_dirpath "$ABI_PSPDIR"
pseudos "01h.bare"

The relevant output is

          spgroup         151
           symrel      1  0  0   0  1  0   0  0  1      -1 -1  0   1  0  0   0  0  1
                       0 -1  0  -1  0  0   0  0 -1       0  1  0  -1 -1  0   0  0  1
                      -1  0  0   1  1  0   0  0 -1       1  1  0   0 -1  0   0  0 -1
            tnons      0.0000000  0.0000000  0.0000000     0.0000000  0.0000000 -0.3333333
                       0.0000000  0.0000000  0.0000000     0.0000000  0.0000000  0.3333333
                       0.0000000  0.0000000 -0.3333333     0.0000000  0.0000000  0.3333333
...
             xred      1.5000000000E-01  3.0000000000E-01  6.6666666667E-01
                       1.5000000000E-01  8.5000000000E-01  3.3333333333E-01
                       7.0000000000E-01  8.5000000000E-01  3.3333333333E-01
                       7.0000000000E-01  8.5000000000E-01  0.0000000000E+00
                       1.5000000000E-01  3.0000000000E-01 -2.2204460493E-16
                       1.5000000000E-01  8.5000000000E-01  6.6666666667E-01

As you can see, the last position in xred is different from the first (original) one, while, according to operation 5 in the Bilbao server
https://www.cryst.ehu.es/cgi-bin/cryst/programs//nph-getgen?gnum=151&what=gp
it should be the same. Moreover, the matrix+translation in operation 5 in Bilbao (and in the online IUCr tables) is not seen in the symrel+tnons output.

Am I missing something or are the symmetry operations not correctly implemented for this space group?

Thanks for any assistance and reading this far!

Xavier

Edit

I have just noticed that changing xred in the example to
xred 0.30 0.15 0.666666666666667
provides the right multiplicity. Then the problem might be that the symmetry axes implicit in abinit do not match those in the current IUCr tables, at least for this space group. I do not have access to the 1983 version of the tables, so I don’t know whether the operations are the same or not.

Yes it looks to me like the abinit internal x and y directions are swapped compared to IUCR. From your input I find xred 0.30 0.15 2/3 to have a multiplicity of 3, but this is not Wyckoff site a in IUCR. xred 0.15 0.30 2/3 is site a according to Wyckoff, but abinit is getting this as multiplicity 6 (so Wyckoff site c). I’ve debugged this kind of thing in abinit before so I’ll have a look. Thanks for posting.