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The ternary germanide Mg5.57Ni16Ge7.43 (cubic, space group Fm\overline{3}m, cF116) belongs to the structural family based on the Th6Mn23-type. The Ge1 and Ge2 atoms fully occupy the 4a (m\overline{3}m symmetry) and 24d (m.mm) sites, respectively. The Ni1 and Ni2 atoms both fully occupy two 32f sites (.3m symmetry). The Mg/Ge statistical mixture occupies the 24e site with 4m.m symmetry. The structure of the title com­pound contains a three-core-shell cluster. At (0,0,0), there is a Ge1 atom which is surrounded by eight Ni atoms at the vertices of a cube and consequently six Mg atoms at the vertices of an octa­hedron. These surrounded eight Ni and six Mg atoms form a [Ge1Ni8(Mg/Ge)6] rhombic dodeca­hedron with a coordination number of 14. The [GeNi8(Mg/Ge)6] rhombic dodeca­hedron is encapsulated within the [Ni24] rhombicubocta­hedron, which is again encapsulated within an [Ni32(Mg/Ge)24] penta­conta­tetra­hedron; thus, the three-core-shell cluster [GeNi8(Mg/Ge)6@Ni24@Ni32(Mg/Ge)24] results. The penta­conta­tetra­hedron is a new representative of Pavlyuk's polyhedra group based on penta­gonal, tetra­gonal and trigonal faces. The dominance of the metallic type of bonding between atoms in the Mg5.57Ni16Ge7.43 structure is confirmed by the results of the electronic structure calculations. The hydrogen sorption capacity of this inter­metallic at 570 K reaches 0.70 wt% H2.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229624003140/yp3234sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2053229624003140/yp3234Isup2.hkl
Contains datablock I

CCDC reference: 2347669

Computing details top

Magnesium nickel germanide top
Crystal data top
Mg5.57Ni16Ge7.43Mo Kα radiation, λ = 0.71073 Å
Mr = 6454.98Cell parameters from 131 reflections
Cubic, Fm3mθ = 3.1–28.3°
a = 11.5036 (6) ŵ = 33.85 mm1
V = 1522.3 (2) Å3T = 293 K
Z = 1Prism, metallic light grey
F(000) = 3010.10.06 × 0.05 × 0.03 mm
Dx = 7.041 Mg m3
Data collection top
Oxford Diffraction Xcalibur3 CCD
diffractometer
120 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.074
ω scansθmax = 28.3°, θmin = 3.1°
Absorption correction: analytical
(CrysAlis RED; Oxford Diffraction, 2008)
h = 1515
Tmin = 0.470, Tmax = 0.683k = 1515
12619 measured reflectionsl = 1515
131 independent reflections
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.013 w = 1/[σ2(Fo2) + 35.3811P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.028(Δ/σ)max < 0.001
S = 1.25Δρmax = 0.63 e Å3
131 reflectionsΔρmin = 0.63 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Ge10.00000.00000.00000.0040 (4)
Ge20.00000.25000.25000.00442 (18)
Ni10.33129 (4)0.33129 (4)0.33129 (4)0.00491 (19)
Ni20.11860 (4)0.11860 (4)0.11860 (4)0.00509 (19)
Mg0.2959 (2)0.00000.00000.0048 (4)0.929 (4)
Ge0.2959 (2)0.00000.00000.0048 (4)0.071 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ge10.0040 (4)0.0040 (4)0.0040 (4)0.0000.0000.000
Ge20.0039 (4)0.0047 (2)0.0047 (2)0.0000.0000.0002 (3)
Ni10.00491 (19)0.00491 (19)0.00491 (19)0.00057 (18)0.00057 (18)0.00057 (18)
Ni20.00509 (19)0.00509 (19)0.00509 (19)0.00015 (18)0.00015 (18)0.00015 (18)
Mg0.0073 (10)0.0035 (6)0.0035 (6)0.0000.0000.000
Ge0.0073 (10)0.0035 (6)0.0035 (6)0.0000.0000.000
Geometric parameters (Å, º) top
Ge1—Ni22.3631 (8)Ni1—Ni1x2.6450 (14)
Ge1—Ni2i2.3632 (8)Ni1—Ni1xii2.6450 (14)
Ge1—Ni2ii2.3632 (8)Ni1—Gexx2.7747 (7)
Ge1—Ni2iii2.3632 (8)Ni1—Mgxxi2.7747 (7)
Ge1—Ni2iv2.3632 (8)Ni1—Mgxxii2.7747 (7)
Ge1—Ni2v2.3632 (8)Ni2—Ge2xvii2.5359 (3)
Ge1—Ni2vi2.3632 (8)Ni2—Ge2xv2.5359 (3)
Ge1—Ni2vii2.3632 (8)Ni2—Ni1ix2.5789 (7)
Ge2—Ni1viii2.3485 (1)Ni2—Ni1xii2.5789 (7)
Ge2—Ni1ix2.3485 (1)Ni2—Ni1x2.5789 (7)
Ge2—Ni1x2.3485 (1)Ni2—Ni2ii2.7288 (9)
Ge2—Ni1xi2.3485 (1)Ni2—Ni2vi2.7288 (9)
Ge2—Ni2ii2.5359 (3)Ni2—Ni2iv2.7288 (9)
Ge2—Ni2xii2.5359 (3)Ni2—Gexvii2.8075 (17)
Ge2—Ni2xiii2.5359 (3)Ni2—Gexv2.8075 (17)
Ge2—Ni22.5359 (3)Mg—Ni1xii2.7747 (7)
Ge2—Gexiv2.9239 (4)Mg—Ni1xxiii2.7747 (7)
Ge2—Mgxv2.9239 (4)Mg—Ni1xxiv2.7747 (7)
Ge2—Mgxvi2.9239 (4)Mg—Ni1xxv2.7747 (7)
Ge2—Mgxvii2.9239 (4)Mg—Ni2vii2.8075 (17)
Ni1—Ge2xviii2.3485 (1)Mg—Ni2vi2.8075 (17)
Ni1—Ge2x2.3485 (1)Mg—Ni2iv2.8075 (17)
Ni1—Ge2xix2.3485 (1)Mg—Ge2xxvi2.9239 (4)
Ni1—Ni2x2.5788 (7)Mg—Ge2xxvii2.9239 (4)
Ni1—Ni2xii2.5788 (7)Mg—Ge2xv2.9239 (4)
Ni1—Ni2ix2.5788 (7)Mg—Ge2xvii2.9239 (4)
Ni1—Ni1ix2.6450 (14)
Ni2—Ge1—Ni2i180.00 (4)Ni1x—Ni1—Mgxxi113.00 (4)
Ni2—Ge1—Ni2ii70.5Ni1xii—Ni1—Mgxxi171.56 (5)
Ni2i—Ge1—Ni2ii109.5Gexx—Ni1—Mgxxi73.5
Ni2—Ge1—Ni2iii109.5Ge2xviii—Ni1—Mgxxii69.03 (2)
Ni2i—Ge1—Ni2iii70.5Ge2x—Ni1—Mgxxii69.03 (2)
Ni2ii—Ge1—Ni2iii70.5Ge2xix—Ni1—Mgxxii132.71 (6)
Ni2—Ge1—Ni2iv70.5Ni2x—Ni1—Mgxxii122.689 (18)
Ni2i—Ge1—Ni2iv109.5Ni2xii—Ni1—Mgxxii122.689 (18)
Ni2ii—Ge1—Ni2iv109.5Ni2ix—Ni1—Mgxxii63.13 (5)
Ni2iii—Ge1—Ni2iv180.00 (6)Ni1ix—Ni1—Mgxxii171.56 (5)
Ni2—Ge1—Ni2v109.5Ni1x—Ni1—Mgxxii113.00 (4)
Ni2i—Ge1—Ni2v70.529 (1)Ni1xii—Ni1—Mgxxii113.00 (4)
Ni2ii—Ge1—Ni2v70.5Gexx—Ni1—Mgxxii73.5
Ni2iii—Ge1—Ni2v109.5Mgxxi—Ni1—Mgxxii73.51 (7)
Ni2iv—Ge1—Ni2v70.5Ge1—Ni2—Ge2xvii112.187 (17)
Ni2—Ge1—Ni2vi70.5Ge1—Ni2—Ge2112.187 (17)
Ni2i—Ge1—Ni2vi109.5Ge2xvii—Ni2—Ge2106.624 (19)
Ni2ii—Ge1—Ni2vi109.5Ge1—Ni2—Ge2xv112.187 (17)
Ni2iii—Ge1—Ni2vi70.5Ge2xvii—Ni2—Ge2xv106.624 (19)
Ni2iv—Ge1—Ni2vi109.5Ge2—Ni2—Ge2xv106.624 (19)
Ni2v—Ge1—Ni2vi180.00 (6)Ge1—Ni2—Ni1ix143.69 (2)
Ni2—Ge1—Ni2vii109.5Ge2xvii—Ni2—Ni1ix54.658 (12)
Ni2i—Ge1—Ni2vii70.5Ge2—Ni2—Ni1ix54.658 (12)
Ni2ii—Ge1—Ni2vii180.00 (4)Ge2xv—Ni2—Ni1ix104.12 (3)
Ni2iii—Ge1—Ni2vii109.5Ge1—Ni2—Ni1xii143.69 (2)
Ni2iv—Ge1—Ni2vii70.5Ge2xvii—Ni2—Ni1xii54.658 (12)
Ni2v—Ge1—Ni2vii109.5Ge2—Ni2—Ni1xii104.12 (3)
Ni2vi—Ge1—Ni2vii70.5Ge2xv—Ni2—Ni1xii54.658 (12)
Ni1viii—Ge2—Ni1ix180.0Ni1ix—Ni2—Ni1xii61.70 (3)
Ni1viii—Ge2—Ni1x111.46 (4)Ge1—Ni2—Ni1x143.69 (2)
Ni1ix—Ge2—Ni1x68.54 (4)Ge2xvii—Ni2—Ni1x104.12 (3)
Ni1viii—Ge2—Ni1xi68.54 (4)Ge2—Ni2—Ni1x54.658 (12)
Ni1ix—Ge2—Ni1xi111.46 (4)Ge2xv—Ni2—Ni1x54.658 (12)
Ni1x—Ge2—Ni1xi180.0Ni1ix—Ni2—Ni1x61.70 (3)
Ni1viii—Ge2—Ni2ii63.601 (15)Ni1xii—Ni2—Ni1x61.70 (3)
Ni1ix—Ge2—Ni2ii116.399 (15)Ge1—Ni2—Ni2ii54.7
Ni1x—Ge2—Ni2ii116.399 (15)Ge2xvii—Ni2—Ni2ii126.587 (8)
Ni1xi—Ge2—Ni2ii63.601 (15)Ge2—Ni2—Ni2ii57.451 (17)
Ni1viii—Ge2—Ni2xii116.399 (15)Ge2xv—Ni2—Ni2ii126.587 (8)
Ni1ix—Ge2—Ni2xii63.601 (15)Ni1ix—Ni2—Ni2ii102.914 (14)
Ni1x—Ge2—Ni2xii63.601 (15)Ni1xii—Ni2—Ni2ii161.57 (2)
Ni1xi—Ge2—Ni2xii116.399 (15)Ni1x—Ni2—Ni2ii102.914 (14)
Ni2ii—Ge2—Ni2xii180.00 (3)Ge1—Ni2—Ni2vi54.7
Ni1viii—Ge2—Ni2xiii63.601 (15)Ge2xvii—Ni2—Ni2vi126.587 (8)
Ni1ix—Ge2—Ni2xiii116.399 (15)Ge2—Ni2—Ni2vi126.587 (8)
Ni1x—Ge2—Ni2xiii116.399 (15)Ge2xv—Ni2—Ni2vi57.451 (17)
Ni1xi—Ge2—Ni2xiii63.601 (15)Ni1ix—Ni2—Ni2vi161.57 (2)
Ni2ii—Ge2—Ni2xiii114.90 (3)Ni1xii—Ni2—Ni2vi102.914 (14)
Ni2xii—Ge2—Ni2xiii65.10 (3)Ni1x—Ni2—Ni2vi102.914 (14)
Ni1viii—Ge2—Ni2116.398 (15)Ni2ii—Ni2—Ni2vi90.0
Ni1ix—Ge2—Ni263.602 (15)Ge1—Ni2—Ni2iv54.7
Ni1x—Ge2—Ni263.602 (15)Ge2xvii—Ni2—Ni2iv57.451 (17)
Ni1xi—Ge2—Ni2116.398 (15)Ge2—Ni2—Ni2iv126.587 (8)
Ni2ii—Ge2—Ni265.10 (3)Ge2xv—Ni2—Ni2iv126.587 (8)
Ni2xii—Ge2—Ni2114.90 (3)Ni1ix—Ni2—Ni2iv102.914 (14)
Ni2xiii—Ge2—Ni2180.0Ni1xii—Ni2—Ni2iv102.914 (14)
Ni1viii—Ge2—Gexiv117.61 (2)Ni1x—Ni2—Ni2iv161.57 (2)
Ni1ix—Ge2—Gexiv62.39 (2)Ni2ii—Ni2—Ni2iv90.0
Ni1x—Ge2—Gexiv117.61 (2)Ni2vi—Ni2—Ni2iv90.0
Ni1xi—Ge2—Gexiv62.39 (2)Ge1—Ni2—Gexvii81.85 (4)
Ni2ii—Ge2—Gexiv118.60 (4)Ge2xvii—Ni2—Gexvii165.96 (5)
Ni2xii—Ge2—Gexiv61.40 (4)Ge2—Ni2—Gexvii66.123 (16)
Ni2xiii—Ge2—Gexiv61.40 (4)Ge2xv—Ni2—Gexvii66.123 (16)
Ni2—Ge2—Gexiv118.60 (4)Ni1ix—Ni2—Gexvii114.04 (3)
Ni1viii—Ge2—Mgxv117.61 (2)Ni1xii—Ni2—Gexvii114.04 (3)
Ni1ix—Ge2—Mgxv62.39 (2)Ni1x—Ni2—Gexvii61.84 (4)
Ni1x—Ge2—Mgxv117.61 (2)Ni2ii—Ni2—Gexvii60.92 (2)
Ni1xi—Ge2—Mgxv62.39 (2)Ni2vi—Ni2—Gexvii60.92 (2)
Ni2ii—Ge2—Mgxv61.40 (4)Ni2iv—Ni2—Gexvii136.59 (4)
Ni2xii—Ge2—Mgxv118.60 (4)Ge1—Ni2—Gexv81.85 (4)
Ni2xiii—Ge2—Mgxv118.60 (4)Ge2xvii—Ni2—Gexv66.123 (16)
Ni2—Ge2—Mgxv61.40 (4)Ge2—Ni2—Gexv66.123 (16)
Gexiv—Ge2—Mgxv69.2Ge2xv—Ni2—Gexv165.96 (5)
Ni1viii—Ge2—Mgxvi62.39 (2)Ni1ix—Ni2—Gexv61.84 (4)
Ni1ix—Ge2—Mgxvi117.61 (2)Ni1xii—Ni2—Gexv114.04 (3)
Ni1x—Ge2—Mgxvi62.39 (2)Ni1x—Ni2—Gexv114.04 (3)
Ni1xi—Ge2—Mgxvi117.61 (2)Ni2ii—Ni2—Gexv60.92 (2)
Ni2ii—Ge2—Mgxvi118.60 (4)Ni2vi—Ni2—Gexv136.59 (4)
Ni2xii—Ge2—Mgxvi61.40 (4)Ni2iv—Ni2—Gexv60.92 (2)
Ni2xiii—Ge2—Mgxvi61.40 (4)Gexvii—Ni2—Gexv118.025 (17)
Ni2—Ge2—Mgxvi118.60 (4)Ni1xii—Mg—Ni1xxiii163.12 (10)
Gexiv—Ge2—Mgxvi110.8Ni1xii—Mg—Ni1xxiv88.766 (14)
Mgxv—Ge2—Mgxvi180.0Ni1xxiii—Mg—Ni1xxiv88.766 (14)
Ni1viii—Ge2—Mgxvii62.39 (2)Ni1xii—Mg—Ni1xxv88.766 (14)
Ni1ix—Ge2—Mgxvii117.61 (2)Ni1xxiii—Mg—Ni1xxv88.766 (14)
Ni1x—Ge2—Mgxvii62.39 (2)Ni1xxiv—Mg—Ni1xxv163.12 (10)
Ni1xi—Ge2—Mgxvii117.61 (2)Ni1xii—Mg—Ni255.03 (2)
Ni2ii—Ge2—Mgxvii61.40 (4)Ni1xxiii—Mg—Ni2141.85 (8)
Ni2xii—Ge2—Mgxvii118.60 (4)Ni1xxiv—Mg—Ni296.12 (3)
Ni2xiii—Ge2—Mgxvii118.60 (4)Ni1xxv—Mg—Ni296.12 (3)
Ni2—Ge2—Mgxvii61.40 (4)Ni1xii—Mg—Ni2vii141.85 (8)
Gexiv—Ge2—Mgxvii180.0Ni1xxiii—Mg—Ni2vii55.03 (2)
Mgxv—Ge2—Mgxvii110.80 (9)Ni1xxiv—Mg—Ni2vii96.12 (3)
Mgxvi—Ge2—Mgxvii69.20 (9)Ni1xxv—Mg—Ni2vii96.12 (3)
Ge2xviii—Ni1—Ge2x119.970 (1)Ni2—Mg—Ni2vii86.83 (7)
Ge2xviii—Ni1—Ge2xix119.970 (1)Ni1xii—Mg—Ni2vi96.12 (3)
Ge2x—Ni1—Ge2xix119.970 (1)Ni1xxiii—Mg—Ni2vi96.12 (3)
Ge2xviii—Ni1—Ni2x164.15 (4)Ni1xxiv—Mg—Ni2vi141.85 (8)
Ge2x—Ni1—Ni2x61.740 (4)Ni1xxv—Mg—Ni2vi55.03 (2)
Ge2xix—Ni1—Ni2x61.740 (4)Ni2—Mg—Ni2vi58.15 (4)
Ge2xviii—Ni1—Ni2xii61.740 (4)Ni2vii—Mg—Ni2vi58.15 (4)
Ge2x—Ni1—Ni2xii164.15 (4)Ni1xii—Mg—Ni2iv96.12 (3)
Ge2xix—Ni1—Ni2xii61.740 (4)Ni1xxiii—Mg—Ni2iv96.12 (3)
Ni2x—Ni1—Ni2xii111.970 (18)Ni1xxiv—Mg—Ni2iv55.03 (2)
Ge2xviii—Ni1—Ni2ix61.740 (4)Ni1xxv—Mg—Ni2iv141.85 (8)
Ge2x—Ni1—Ni2ix61.740 (4)Ni2—Mg—Ni2iv58.15 (4)
Ge2xix—Ni1—Ni2ix164.15 (4)Ni2vii—Mg—Ni2iv58.15 (4)
Ni2x—Ni1—Ni2ix111.970 (18)Ni2vi—Mg—Ni2iv86.83 (7)
Ni2xii—Ni1—Ni2ix111.970 (18)Ni1xii—Mg—Ge2xxvi135.598 (4)
Ge2xviii—Ni1—Ni1ix107.624 (17)Ni1xxiii—Mg—Ge2xxvi48.589 (5)
Ge2x—Ni1—Ni1ix107.624 (17)Ni1xxiv—Mg—Ge2xxvi48.589 (5)
Ge2xix—Ni1—Ni1ix55.73 (2)Ni1xxv—Mg—Ge2xxvi135.598 (4)
Ni2x—Ni1—Ni1ix59.148 (17)Ni2—Mg—Ge2xxvi110.29 (6)
Ni2xii—Ni1—Ni1ix59.148 (17)Ni2vii—Mg—Ge2xxvi52.47 (2)
Ni2ix—Ni1—Ni1ix108.43 (2)Ni2vi—Mg—Ge2xxvi110.29 (6)
Ge2xviii—Ni1—Ni1x55.73 (2)Ni2iv—Mg—Ge2xxvi52.47 (2)
Ge2x—Ni1—Ni1x107.624 (17)Ni1xii—Mg—Ge2xxvii135.598 (4)
Ge2xix—Ni1—Ni1x107.624 (17)Ni1xxiii—Mg—Ge2xxvii48.589 (5)
Ni2x—Ni1—Ni1x108.43 (2)Ni1xxiv—Mg—Ge2xxvii135.598 (4)
Ni2xii—Ni1—Ni1x59.148 (17)Ni1xxv—Mg—Ge2xxvii48.589 (5)
Ni2ix—Ni1—Ni1x59.148 (17)Ni2—Mg—Ge2xxvii110.29 (6)
Ni1ix—Ni1—Ni1x60.0Ni2vii—Mg—Ge2xxvii52.47 (2)
Ge2xviii—Ni1—Ni1xii107.624 (17)Ni2vi—Mg—Ge2xxvii52.47 (2)
Ge2x—Ni1—Ni1xii55.73 (2)Ni2iv—Mg—Ge2xxvii110.29 (6)
Ge2xix—Ni1—Ni1xii107.624 (17)Ge2xxvi—Mg—Ge2xxvii88.132 (16)
Ni2x—Ni1—Ni1xii59.148 (17)Ni1xii—Mg—Ge2xv48.589 (5)
Ni2xii—Ni1—Ni1xii108.43 (2)Ni1xxiii—Mg—Ge2xv135.598 (4)
Ni2ix—Ni1—Ni1xii59.148 (17)Ni1xxiv—Mg—Ge2xv135.598 (4)
Ni1ix—Ni1—Ni1xii60.0Ni1xxv—Mg—Ge2xv48.589 (5)
Ni1x—Ni1—Ni1xii60.0Ni2—Mg—Ge2xv52.47 (2)
Ge2xviii—Ni1—Gexx132.71 (6)Ni2vii—Mg—Ge2xv110.29 (6)
Ge2x—Ni1—Gexx69.03 (2)Ni2vi—Mg—Ge2xv52.47 (2)
Ge2xix—Ni1—Gexx69.03 (2)Ni2iv—Mg—Ge2xv110.29 (6)
Ni2x—Ni1—Gexx63.13 (5)Ge2xxvi—Mg—Ge2xv159.20 (9)
Ni2xii—Ni1—Gexx122.689 (18)Ge2xxvii—Mg—Ge2xv88.132 (16)
Ni2ix—Ni1—Gexx122.689 (18)Ni1xii—Mg—Ge2xvii48.589 (5)
Ni1ix—Ni1—Gexx113.00 (4)Ni1xxiii—Mg—Ge2xvii135.598 (4)
Ni1x—Ni1—Gexx171.56 (5)Ni1xxiv—Mg—Ge2xvii48.589 (5)
Ni1xii—Ni1—Gexx113.00 (4)Ni1xxv—Mg—Ge2xvii135.598 (4)
Ge2xviii—Ni1—Mgxxi69.03 (2)Ni2—Mg—Ge2xvii52.47 (2)
Ge2x—Ni1—Mgxxi132.71 (6)Ni2vii—Mg—Ge2xvii110.29 (6)
Ge2xix—Ni1—Mgxxi69.03 (2)Ni2vi—Mg—Ge2xvii110.29 (6)
Ni2x—Ni1—Mgxxi122.689 (18)Ni2iv—Mg—Ge2xvii52.47 (2)
Ni2xii—Ni1—Mgxxi63.13 (5)Ge2xxvi—Mg—Ge2xvii88.132 (16)
Ni2ix—Ni1—Mgxxi122.689 (18)Ge2xxvii—Mg—Ge2xvii159.20 (9)
Ni1ix—Ni1—Mgxxi113.00 (4)Ge2xv—Mg—Ge2xvii88.132 (16)
Symmetry codes: (i) x, y, z; (ii) x, y, z; (iii) x, y, z; (iv) x, y, z; (v) x, y, z; (vi) x, y, z; (vii) x, y, z; (viii) x1/2, y+1/2, z; (ix) x+1/2, y, z+1/2; (x) x+1/2, y+1/2, z; (xi) x1/2, y, z+1/2; (xii) x, y+1/2, z+1/2; (xiii) x, y+1/2, z+1/2; (xiv) y, z+1/2, x+1/2; (xv) z, x, y; (xvi) z, x+1/2, y+1/2; (xvii) y, z, x; (xviii) y+1/2, z, x+1/2; (xix) z, x+1/2, y+1/2; (xx) y+1/2, z+1/2, x; (xxi) x, y+1/2, z+1/2; (xxii) z+1/2, x, y+1/2; (xxiii) x, y1/2, z1/2; (xxiv) x, y+1/2, z1/2; (xxv) x, y1/2, z+1/2; (xxvi) z, x, y; (xxvii) y+1/2, z1/2, x.
 

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