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Single crystals of triiron(II) tetrairon(III) hexakis­[orthoarsenate(V)], Fe7(AsO4)6, were grown by chemical transport reactions. The structure is isotypic with other MII3MIII4(XO4)6 compounds (M = first row transition metals; X = P, V) which adopt the Fe7(PO4)6 structure type. The structure includes four independent cation sites, two of which are occupied by divalent and two by trivalent iron cations. Slightly distorted [FeO6] octahedra and [FeO5] trigonal bipyramids share edges and form infinite chains, which are linked by corner-sharing with AsO4 tetrahedra and with [FeO6] octahedra into a three-dimensional network. Except for one Fe site with \overline 1 symmetry occupied by a divalent iron cation, all other atoms are located in general positions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536804026182/br6166sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536804026182/br6166Isup2.hkl
Contains datablock I

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](Fe-O) = 0.002 Å
  • R factor = 0.021
  • wR factor = 0.048
  • Data-to-parameter ratio = 23.0

checkCIF/PLATON results

No syntax errors found


No errors found in this datablock

Computing details top

Data collection: CAD-4 Software (Enraf-Nonius, 1989); cell refinement: CAD-4 Software; data reduction: HELENA implemented in PLATON (Spek, 2002); program(s) used to solve structure: from the coordinates of Gorbunov et al. (1980); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ATOMS (Dowty, 2000); software used to prepare material for publication: SHELXL97.

Triiron(II) tetrairon (III) hexakisorthoarsenate(V) top
Crystal data top
Fe7(AsO4)6Z = 1
Mr = 1224.47F(000) = 572
Triclinic, P1Dx = 4.540 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 6.5738 (6) ÅCell parameters from 25 reflections
b = 8.0973 (9) Åθ = 13.7–17.9°
c = 9.6190 (6) ŵ = 16.64 mm1
α = 104.843 (7)°T = 293 K
β = 107.936 (6)°Block, black
γ = 101.842 (9)°0.40 × 0.29 × 0.14 mm
V = 447.85 (8) Å3
Data collection top
Enraf–Nonius CAD-4
diffractometer
3589 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.024
Graphite monochromatorθmax = 35.0°, θmin = 2.4°
ω/2θ scansh = 1010
Absorption correction: numerical
(HABITUS; Herrendorf, 1993-1997)
k = 1313
Tmin = 0.022, Tmax = 0.266l = 1515
7836 measured reflections3 standard reflections every 300 min
3918 independent reflections intensity decay: none
Refinement top
Refinement on F2Primary atom site location: isomorphous structure methods
Least-squares matrix: full w = 1/[σ2(Fo2) + (0.0213P)2 + 0.3318P]
where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.021(Δ/σ)max = 0.001
wR(F2) = 0.048Δρmax = 1.05 e Å3
S = 1.16Δρmin = 1.12 e Å3
3918 reflectionsExtinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
170 parametersExtinction coefficient: 0.0387 (8)
0 restraints
Special details top

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

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Fe10.04429 (4)0.21905 (4)0.02428 (3)0.00576 (5)
Fe20.27791 (4)0.30598 (4)0.78591 (3)0.00756 (5)
Fe30.61854 (4)0.04663 (4)0.38694 (3)0.00539 (5)
Fe40.00000.50000.50000.00820 (7)
As10.09889 (3)0.09851 (2)0.33515 (2)0.00456 (4)
As20.22972 (3)0.65095 (2)0.27056 (2)0.00464 (4)
As30.60165 (3)0.26719 (2)0.12624 (2)0.00507 (4)
O10.0104 (2)0.6977 (2)0.15721 (16)0.0085 (2)
O20.0672 (2)0.04996 (19)0.14577 (15)0.0077 (2)
O30.1298 (2)0.03464 (19)0.65593 (16)0.0077 (2)
O40.1344 (3)0.3082 (2)0.42980 (19)0.0134 (3)
O50.2090 (3)0.4370 (2)0.19878 (18)0.0118 (2)
O60.2250 (2)0.70213 (19)0.45259 (16)0.0079 (2)
O70.3220 (2)0.03165 (19)0.41751 (16)0.0067 (2)
O80.5256 (2)0.22562 (19)0.72296 (16)0.0073 (2)
O90.5524 (3)0.1248 (2)0.21822 (18)0.0137 (3)
O100.6470 (2)0.7427 (2)0.00272 (16)0.0090 (2)
O110.7379 (2)0.4727 (2)0.26302 (17)0.0103 (2)
O120.7557 (2)0.2149 (2)0.02408 (18)0.0138 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00552 (10)0.00603 (10)0.00569 (10)0.00182 (8)0.00199 (8)0.00211 (8)
Fe20.00772 (10)0.00636 (11)0.00962 (11)0.00272 (8)0.00438 (9)0.00263 (9)
Fe30.00512 (10)0.00577 (11)0.00541 (10)0.00156 (8)0.00213 (8)0.00206 (8)
Fe40.00996 (15)0.00604 (15)0.00992 (16)0.00331 (12)0.00505 (12)0.00266 (13)
As10.00419 (7)0.00505 (8)0.00442 (7)0.00184 (5)0.00152 (6)0.00145 (6)
As20.00390 (7)0.00471 (7)0.00449 (7)0.00089 (5)0.00125 (5)0.00103 (6)
As30.00423 (7)0.00557 (8)0.00513 (8)0.00150 (5)0.00123 (6)0.00207 (6)
O10.0057 (5)0.0131 (6)0.0091 (6)0.0048 (4)0.0025 (4)0.0066 (5)
O20.0117 (5)0.0067 (5)0.0048 (5)0.0029 (4)0.0028 (4)0.0027 (4)
O30.0050 (5)0.0080 (5)0.0096 (6)0.0008 (4)0.0042 (4)0.0018 (5)
O40.0172 (6)0.0060 (6)0.0172 (7)0.0048 (5)0.0085 (5)0.0007 (5)
O50.0152 (6)0.0057 (6)0.0105 (6)0.0031 (5)0.0027 (5)0.0007 (5)
O60.0103 (5)0.0065 (5)0.0059 (5)0.0003 (4)0.0041 (4)0.0012 (4)
O70.0046 (5)0.0096 (6)0.0071 (5)0.0038 (4)0.0018 (4)0.0042 (5)
O80.0048 (5)0.0059 (5)0.0099 (6)0.0003 (4)0.0036 (4)0.0012 (4)
O90.0163 (6)0.0118 (6)0.0104 (6)0.0002 (5)0.0013 (5)0.0076 (5)
O100.0063 (5)0.0149 (6)0.0076 (6)0.0049 (5)0.0024 (4)0.0057 (5)
O110.0113 (5)0.0058 (5)0.0093 (6)0.0003 (4)0.0010 (5)0.0007 (5)
O120.0081 (5)0.0213 (8)0.0120 (6)0.0063 (5)0.0058 (5)0.0020 (6)
Geometric parameters (Å, º) top
Fe1—O12i1.8896 (14)As3—O111.6860 (15)
Fe1—O51.9191 (15)As3—O10iii1.6924 (13)
Fe1—O1ii1.9867 (14)As3—Fe2vi3.2023 (5)
Fe1—O22.0147 (14)As3—Fe1xii3.4071 (4)
Fe1—O10iii2.0950 (13)As3—Fe2v3.4431 (4)
Fe1—O2iv2.1768 (14)As3—Fe4xii3.4698 (5)
Fe1—Fe2v3.2655 (4)As3—Fe3xiii4.5367 (6)
Fe1—As13.3168 (4)As3—Fe1iv4.6968 (7)
Fe2—O11vi1.9808 (16)O1—Fe1ii1.9867 (14)
Fe2—O82.0693 (13)O1—Fe2vii2.1251 (13)
Fe2—O32.0744 (15)O1—Fe3xi3.9462 (15)
Fe2—O10vi2.0987 (14)O1—Fe3vi4.0189 (15)
Fe2—O1vii2.1251 (13)O2—Fe1iv2.1768 (14)
Fe2—As3vi3.2023 (5)O2—Fe2x3.6181 (15)
Fe2—Fe3viii3.2314 (5)O3—As1x1.7007 (13)
Fe2—Fe1ix3.2655 (4)O3—Fe3viii2.0166 (13)
Fe3—O91.8514 (15)O3—Fe3i3.5928 (14)
Fe3—O3viii2.0166 (13)O3—Fe1ix3.7365 (14)
Fe3—O6vi2.0332 (14)O3—Fe4xiv4.0109 (15)
Fe3—O72.0432 (12)O3—Fe2x4.0986 (15)
Fe3—O8viii2.0510 (14)O4—Fe3i3.4496 (16)
Fe3—O7viii2.0863 (14)O4—Fe3viii4.0920 (17)
Fe3—Fe3viii3.1900 (5)O5—Fe2vi3.5195 (16)
Fe3—Fe2viii3.2314 (5)O5—Fe2v4.0311 (16)
Fe4—O42.0107 (14)O6—Fe3vi2.0332 (14)
Fe4—O4vii2.0107 (14)O6—Fe2vii3.3702 (15)
Fe4—O6vii2.2087 (14)O6—Fe3xi3.7176 (14)
Fe4—O62.2087 (14)O7—Fe3viii2.0863 (14)
Fe4—O11vi2.3194 (15)O7—Fe2x3.8650 (15)
Fe4—O11i2.3194 (15)O7—Fe1iv3.9051 (14)
Fe4—As23.3648 (3)O8—As2vi1.6842 (13)
Fe4—As2vii3.3648 (3)O8—Fe3viii2.0510 (14)
As1—O41.6371 (15)O8—Fe1xv3.7544 (14)
As1—O21.6977 (13)O9—Fe4xii3.5265 (17)
As1—O3x1.7007 (13)O9—Fe2viii3.8686 (17)
As1—O71.7037 (13)O9—Fe1iv3.8900 (17)
As1—Fe3i3.3057 (4)O10—As3iii1.6924 (13)
As1—Fe2x3.3404 (6)O10—Fe1iii2.0950 (13)
As1—Fe3viii3.3801 (4)O10—Fe2vi2.0987 (14)
As1—Fe1iv3.4494 (5)O10—Fe2v3.5106 (16)
As2—O51.6519 (15)O10—Fe3xi3.9631 (15)
As2—O8vi1.6842 (13)O10—Fe1xvi4.1067 (16)
As2—O11.6965 (13)O11—Fe2vi1.9808 (15)
As2—O61.7046 (13)O11—Fe4xii2.3194 (15)
As2—Fe3vi3.2688 (5)O11—Fe1xii3.9596 (15)
As2—Fe2vii3.3182 (4)O12—Fe1xii1.8896 (14)
As2—Fe3xi3.3303 (6)O12—Fe2v3.6117 (16)
As2—Fe1ii3.3996 (4)O12—Fe3xiii3.7080 (16)
As2—Fe2vi3.4074 (4)O12—Fe2vi3.9256 (17)
As3—O121.6575 (14)O12—Fe1xiii3.9655 (17)
As3—O91.6624 (16)
O12i—Fe1—O596.74 (7)Fe3viii—O3—Fe2x86.36 (4)
O12i—Fe1—O1ii91.71 (6)Fe2—O3—Fe2x141.37 (6)
O5—Fe1—O1ii103.38 (7)Fe3i—O3—Fe2x49.15 (2)
O12i—Fe1—O291.23 (7)Fe1ix—O3—Fe2x135.10 (3)
O5—Fe1—O296.67 (6)Fe4xiv—O3—Fe2x54.23 (2)
O1ii—Fe1—O2159.24 (6)As1—O4—Fe4149.02 (10)
O12i—Fe1—O10iii168.34 (7)As1—O4—Fe2100.61 (7)
O5—Fe1—O10iii82.48 (6)Fe4—O4—Fe285.42 (5)
O1ii—Fe1—O10iii77.22 (5)As1—O4—Fe3i71.13 (5)
O2—Fe1—O10iii100.42 (6)Fe4—O4—Fe3i79.62 (5)
O12i—Fe1—O2iv94.98 (6)Fe2—O4—Fe3i82.98 (4)
O5—Fe1—O2iv164.92 (6)As1—O4—Fe166.45 (5)
O1ii—Fe1—O2iv85.70 (6)Fe4—O4—Fe1109.59 (6)
O2—Fe1—O2iv73.58 (6)Fe2—O4—Fe1164.99 (5)
O10iii—Fe1—O2iv87.93 (6)Fe3i—O4—Fe199.03 (4)
O11vi—Fe2—O8107.71 (6)As1—O4—Fe3viii53.34 (5)
O11vi—Fe2—O3133.13 (6)Fe4—O4—Fe3viii134.90 (7)
O8—Fe2—O375.12 (5)Fe2—O4—Fe3viii50.59 (2)
O11vi—Fe2—O10vi131.39 (6)Fe3i—O4—Fe3viii84.89 (3)
O8—Fe2—O10vi98.25 (5)Fe1—O4—Fe3viii114.57 (4)
O3—Fe2—O10vi92.57 (6)As2—O5—Fe1144.22 (10)
O11vi—Fe2—O1vii89.04 (6)As2—O5—Fe2vi72.45 (5)
O8—Fe2—O1vii162.01 (6)Fe1—O5—Fe2vi117.65 (6)
O3—Fe2—O1vii88.72 (6)As2—O5—Fe470.35 (5)
O10vi—Fe2—O1vii74.22 (5)Fe1—O5—Fe4115.05 (6)
O9—Fe3—O3viii92.69 (7)Fe2vi—O5—Fe4126.58 (4)
O9—Fe3—O6vi94.58 (7)As2—O5—Fe2v113.26 (7)
O3viii—Fe3—O6vi104.20 (6)Fe1—O5—Fe2v53.20 (4)
O9—Fe3—O797.54 (6)Fe2vi—O5—Fe2v67.02 (3)
O3viii—Fe3—O7159.06 (6)Fe4—O5—Fe2v165.24 (5)
O6vi—Fe3—O793.18 (6)As2—O6—Fe3vi121.73 (7)
O9—Fe3—O8viii100.64 (7)As2—O6—Fe4118.03 (7)
O3viii—Fe3—O8viii76.77 (5)Fe3vi—O6—Fe4119.57 (6)
O6vi—Fe3—O8viii164.70 (6)As2—O6—Fe2vii73.55 (5)
O7—Fe3—O8viii83.39 (5)Fe3vi—O6—Fe2vii108.39 (5)
O9—Fe3—O7viii175.81 (6)Fe4—O6—Fe2vii80.06 (4)
O3viii—Fe3—O7viii91.40 (5)As2—O6—Fe3xi63.60 (4)
O6vi—Fe3—O7viii83.57 (6)Fe3vi—O6—Fe3xi59.03 (3)
O7—Fe3—O7viii78.85 (5)Fe4—O6—Fe3xi177.97 (6)
O8viii—Fe3—O7viii81.14 (6)Fe2vii—O6—Fe3xi101.73 (4)
O4—Fe4—O4vii180.000 (1)As1—O7—Fe3132.08 (8)
O4—Fe4—O6vii87.16 (6)As1—O7—Fe3viii125.92 (7)
O4vii—Fe4—O6vii92.84 (6)Fe3—O7—Fe3viii101.15 (5)
O4—Fe4—O692.84 (6)As1—O7—Fe281.02 (5)
O4vii—Fe4—O687.16 (6)Fe3—O7—Fe2123.77 (5)
O6vii—Fe4—O6180.00 (6)Fe3viii—O7—Fe258.22 (3)
O4—Fe4—O11vi79.72 (6)As1—O7—Fe2x59.51 (4)
O4vii—Fe4—O11vi100.28 (6)Fe3—O7—Fe2x134.95 (6)
O6vii—Fe4—O11vi84.39 (5)Fe3viii—O7—Fe2x91.87 (4)
O6—Fe4—O11vi95.61 (5)Fe2—O7—Fe2x99.81 (3)
O4—Fe4—O11i100.28 (6)As1—O7—Fe1iv61.97 (4)
O4vii—Fe4—O11i79.72 (6)Fe3—O7—Fe1iv93.64 (4)
O6vii—Fe4—O11i95.61 (5)Fe3viii—O7—Fe1iv133.46 (6)
O6—Fe4—O11i84.39 (5)Fe2—O7—Fe1iv140.10 (3)
O11vi—Fe4—O11i180.0Fe2x—O7—Fe1iv49.700 (19)
O4—As1—O2115.81 (8)As2vi—O8—Fe3viii125.86 (7)
O4—As1—O3x108.82 (7)As2vi—O8—Fe2130.12 (8)
O2—As1—O3x108.57 (7)Fe3viii—O8—Fe2103.30 (6)
O4—As1—O7111.60 (8)As2vi—O8—Fe368.73 (4)
O2—As1—O7104.82 (7)Fe3viii—O8—Fe364.56 (4)
O3x—As1—O7106.81 (7)Fe2—O8—Fe3138.99 (6)
O5—As2—O8vi107.68 (7)As2vi—O8—Fe1xv64.85 (4)
O5—As2—O1110.42 (7)Fe3viii—O8—Fe1xv97.97 (5)
O8vi—As2—O1110.42 (7)Fe2—O8—Fe1xv120.66 (5)
O5—As2—O6110.91 (7)Fe3—O8—Fe1xv100.17 (3)
O8vi—As2—O6109.94 (7)As3—O9—Fe3153.39 (10)
O1—As2—O6107.49 (7)As3—O9—Fe4xii74.37 (5)
O12—As3—O9112.76 (9)Fe3—O9—Fe4xii79.32 (5)
O12—As3—O11109.58 (8)As3—O9—Fe168.72 (5)
O9—As3—O11107.08 (8)Fe3—O9—Fe1128.34 (7)
O12—As3—O10iii106.38 (7)Fe4xii—O9—Fe1115.68 (5)
O9—As3—O10iii108.54 (7)As3—O9—Fe2viii129.94 (8)
O11—As3—O10iii112.59 (7)Fe3—O9—Fe2viii56.28 (4)
As2—O1—Fe1ii134.59 (7)Fe4xii—O9—Fe2viii109.05 (4)
As2—O1—Fe2vii120.10 (7)Fe1—O9—Fe2viii135.10 (5)
Fe1ii—O1—Fe2vii105.10 (6)As3—O9—Fe1iv108.78 (6)
As2—O1—Fe162.43 (5)Fe3—O9—Fe1iv97.49 (6)
Fe1ii—O1—Fe1107.67 (5)Fe4xii—O9—Fe1iv162.18 (5)
Fe2vii—O1—Fe1109.82 (5)Fe1—O9—Fe1iv52.93 (2)
As2—O1—Fe3xi56.66 (4)Fe2viii—O9—Fe1iv82.75 (3)
Fe1ii—O1—Fe3xi93.36 (5)As3iii—O10—Fe1iii127.23 (8)
Fe2vii—O1—Fe3xi127.38 (6)As3iii—O10—Fe2vi130.21 (7)
Fe1—O1—Fe3xi110.48 (3)Fe1iii—O10—Fe2vi102.28 (6)
As2—O1—Fe3vi52.27 (4)As3iii—O10—Fe2v65.47 (5)
Fe1ii—O1—Fe3vi132.12 (6)Fe1iii—O10—Fe2v112.48 (6)
Fe2vii—O1—Fe3vi87.14 (4)Fe2vi—O10—Fe2v93.23 (5)
Fe1—O1—Fe3vi111.11 (3)As3iii—O10—Fe3xi98.62 (5)
Fe3xi—O1—Fe3vi47.208 (19)Fe1iii—O10—Fe3xi119.15 (5)
As2—O1—Fe455.25 (4)Fe2vi—O10—Fe3xi54.46 (3)
Fe1ii—O1—Fe4169.69 (6)Fe2v—O10—Fe3xi122.93 (4)
Fe2vii—O1—Fe465.55 (4)As3iii—O10—Fe1xvi99.65 (6)
Fe1—O1—Fe473.11 (3)Fe1iii—O10—Fe1xvi54.56 (4)
Fe3xi—O1—Fe495.96 (3)Fe2vi—O10—Fe1xvi115.01 (5)
Fe3vi—O1—Fe454.20 (2)Fe2v—O10—Fe1xvi150.22 (4)
As1—O2—Fe1126.41 (8)Fe3xi—O10—Fe1xvi83.45 (3)
As1—O2—Fe1iv125.37 (7)As3—O11—Fe2vi121.49 (8)
Fe1—O2—Fe1iv106.42 (6)As3—O11—Fe4xii119.22 (8)
As1—O2—Fe2x66.93 (4)Fe2vi—O11—Fe4xii118.35 (7)
Fe1—O2—Fe2x141.48 (6)As3—O11—Fe359.92 (5)
Fe1iv—O2—Fe2x62.94 (3)Fe2vi—O11—Fe3163.69 (6)
As1—O2—Fe368.53 (4)Fe4xii—O11—Fe365.95 (4)
Fe1—O2—Fe3120.31 (5)As3—O11—Fe1xii58.82 (4)
Fe1iv—O2—Fe398.25 (5)Fe2vi—O11—Fe1xii109.12 (6)
Fe2x—O2—Fe398.18 (3)Fe4xii—O11—Fe1xii92.81 (4)
As1x—O3—Fe3viii125.35 (8)Fe3—O11—Fe1xii85.71 (3)
As1x—O3—Fe2124.17 (7)As3—O12—Fe1xii147.63 (10)
Fe3viii—O3—Fe2104.34 (6)As3—O12—Fe2v70.80 (5)
As1x—O3—Fe3i69.02 (4)Fe1xii—O12—Fe2v135.21 (7)
Fe3viii—O3—Fe3i129.19 (6)As3—O12—Fe3xiii109.41 (6)
Fe2—O3—Fe3i100.06 (5)Fe1xii—O12—Fe3xiii102.85 (6)
As1x—O3—Fe1ix67.05 (4)Fe2v—O12—Fe3xiii52.38 (2)
Fe3viii—O3—Fe1ix132.37 (6)As3—O12—Fe2vi52.61 (5)
Fe2—O3—Fe1ix60.64 (3)Fe1xii—O12—Fe2vi112.84 (7)
Fe3i—O3—Fe1ix98.44 (3)Fe2v—O12—Fe2vi67.41 (3)
As1x—O3—Fe4xiv61.01 (4)Fe3xiii—O12—Fe2vi118.74 (4)
Fe3viii—O3—Fe4xiv65.49 (4)As3—O12—Fe1xiii124.57 (8)
Fe2—O3—Fe4xiv163.06 (6)Fe1xii—O12—Fe1xiii57.65 (5)
Fe3i—O3—Fe4xiv96.79 (3)Fe2v—O12—Fe1xiii132.18 (5)
Fe1ix—O3—Fe4xiv115.12 (4)Fe3xiii—O12—Fe1xiii81.08 (3)
As1x—O3—Fe2x71.73 (5)Fe2vi—O12—Fe1xiii160.16 (5)
Symmetry codes: (i) x1, y, z; (ii) x, y+1, z; (iii) x+1, y+1, z; (iv) x, y, z; (v) x, y, z1; (vi) x+1, y+1, z+1; (vii) x, y+1, z+1; (viii) x+1, y, z+1; (ix) x, y, z+1; (x) x, y, z+1; (xi) x, y+1, z; (xii) x+1, y, z; (xiii) x+1, y, z; (xiv) x, y1, z; (xv) x+1, y, z+1; (xvi) x+1, y+1, z.
 

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