Atomic coordinates can be found in the paper cited (Lamfers et al.) and have been relaxed via DFT. Typical values are given in the following Quantum Espresso input parameter sets: 

ReS2: 
=====

 &control
    calculation='scf',
    restart_mode='from_scratch',
    prefix='res2',
    pseudo_dir = '/home/pysdw/espresso-5.2.0/pseudo',
    outdir='/home/pysdw/espresso-5.2.0/tempdir',
    tprnfor=.true.,
    tstress=.true.,
 /
 &system    
    ibrav=  0, 
    celldm(1)=12.3976,
    nat=  12, ntyp= 2, 
    ecutwfc =50.0,
    ecutrho = 200.0
 /
 &electrons
    conv_thr =  1.0d-12,
    mixing_mode='plain',
    mixing_beta = 0.3,
 /
ATOMIC_SPECIES
 S   32.065     S.pz-n-nc.UPF
 Re  186.21    Re.pz-n-nc.UPF
CELL_PARAMETERS {alat}
   0.962165452  -0.000047315  -0.128125895
  -0.461260038   0.863832945   0.129868320
  -0.133319416  -0.246567453   0.921553875
ATOMIC_POSITIONS {crystal}
Re       0.063150000   0.314770000   0.491380000    0   0   0
Re       0.487230000   0.290420000   0.496810000    0   0   0
S        0.248160000   0.381920000   0.206140000    0   0   0
S        0.720490000   0.339020000   0.238680000    0   0   0
S        0.226100000   0.108620000   0.723660000    0   0   0
S        0.754960000   0.136460000   0.696640000    0   0   0
Re      -0.063150000  -0.314770000  -0.491380000    0   0   0
Re      -0.487230000  -0.290420000  -0.496810000    0   0   0
S       -0.248160000  -0.381920000  -0.206140000    0   0   0
S       -0.720490000  -0.339020000  -0.238680000    0   0   0
S       -0.226100000  -0.108620000  -0.723660000    0   0   0
S       -0.754960000  -0.136460000  -0.696640000    0   0   0
K_POINTS {automatic}
 8 8 8 0 0 0 


ReSe2
=====
&control
    calculation='scf'
    restart_mode='from_scratch',
    prefix='rese2',
    pseudo_dir = '/home/pysdw/pseudo',
    outdir='/home/pysdw/tmp',
 /
 &system    
    ibrav=  14, 
    celldm(1)=12.363,
    celldm(2)=1.0171,  
    celldm(3)=1.0188,
    celldm(4)=-0.03211,
    celldm(5)=-0.25713,
    celldm(6)=-0.48344,
    nat=  12, ntyp= 2, 
    ecutwfc =60.0, 
 /
 &electrons
    conv_thr =  1.0d-12,
    mixing_mode='plain',
    mixing_beta = 0.3,
 /
ATOMIC_SPECIES
 Se   78.96  Se.pw-mt_fhi.UPF
 Re  186.21  Re.pw-mt_fhi.UPF
ATOMIC_POSITIONS {crystal}
Re 0.06315 0.31477 0.49138  0  0  0
Re 0.48723 0.29042 0.49681  0  0  0 
Se 0.24816 0.38192 0.20614  0  0  0 
Se 0.72049 0.33902 0.23868  0  0  0 
Se 0.22610 0.10862 0.72366  0  0  0
Se 0.75496 0.13646 0.69664  0  0  0
Re -0.06315 -0.31477 -0.49138  0  0  0
Re -0.48723 -0.29042 -0.49681  0  0  0 
Se -0.24816 -0.38192 -0.20614  0  0  0 
Se -0.72049 -0.33902 -0.23868  0  0  0 
Se -0.22610 -0.10862 -0.72366  0  0  0
Se -0.75496 -0.13646 -0.69664  0  0  0
K_POINTS {automatic}
10 10 10 0 0 0