Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536805012018/nc6029sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536805012018/nc6029Isup2.hkl |
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (P-O) = 0.002 Å
- R factor = 0.031
- wR factor = 0.084
- Data-to-parameter ratio = 12.5
checkCIF/PLATON results
No syntax errors found
Alert level A PLAT029_ALERT_3_A _diffrn_measured_fraction_theta_full Low ....... 0.92
Alert level C PLAT199_ALERT_1_C Check the Reported _cell_measurement_temperature 293 K PLAT200_ALERT_1_C Check the Reported _diffrn_ambient_temperature . 293 K PLAT222_ALERT_3_C Large Non-Solvent H Ueq(max)/Ueq(min) ... 3.95 Ratio PLAT731_ALERT_1_C Bond Calc 0.89(4), Rep 0.891(19) ...... 2.11 su-Rat N2 -H24 1.555 1.555 PLAT731_ALERT_1_C Bond Calc 0.86(4), Rep 0.866(19) ...... 2.11 su-Rat N6 -H64 1.555 1.555 PLAT735_ALERT_1_C D-H Calc 0.89(4), Rep 0.891(19) ...... 2.11 su-Rat N2 -H24 1.555 1.555 PLAT735_ALERT_1_C D-H Calc 0.86(4), Rep 0.866(19) ...... 2.11 su-Rat N6 -H64 1.555 1.555 PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 4 H4 N PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 5 H4 N PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 6 H4 N PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 7 H4 N PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 10 H4 N
Alert level G REFLT03_ALERT_4_G Please check that the estimate of the number of Friedel pairs is correct. If it is not, please give the correct count in the _publ_section_exptl_refinement section of the submitted CIF. From the CIF: _diffrn_reflns_theta_max 28.13 From the CIF: _reflns_number_total 4004 Count of symmetry unique reflns 2401 Completeness (_total/calc) 166.76% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 1603 Fraction of Friedel pairs measured 0.668 Are heavy atom types Z>Si present yes
1 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 12 ALERT level C = Check and explain 1 ALERT level G = General alerts; check 6 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 0 ALERT type 2 Indicator that the structure model may be wrong or deficient 2 ALERT type 3 Indicator that the structure quality may be low 6 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: IPDS (Stoe & Cie, 1996); cell refinement: IPDS; data reduction: IPDS; program(s) used to solve structure: SIR92 (Altomare et al., 1993); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 1996); software used to prepare material for publication: CIF-Editor (Wieczorrek, 2004).
(NH4)7(HPO4)2(PO4) | F(000) = 440 |
Mr = 413.22 | Dx = 1.523 Mg m−3 |
Monoclinic, P21 | Melting point: unknown K |
Hall symbol: P 2yb | Mo Kα radiation, λ = 0.71073 Å |
a = 10.4667 (17) Å | Cell parameters from 1206 reflections |
b = 6.2976 (7) Å | θ = 1.9–28.2° |
c = 14.072 (2) Å | µ = 0.39 mm−1 |
β = 103.738 (19)° | T = 293 K |
V = 901.0 (2) Å3 | Column, colourless |
Z = 2 | 0.5 × 0.25 × 0.25 mm |
Stoe IPDS I diffractometer | 4004 independent reflections |
Radiation source: fine-focus sealed tube | 3538 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.034 |
Detector resolution: not measured pixels mm-1 | θmax = 28.1°, θmin = 2.8° |
φ scans | h = −13→13 |
Absorption correction: numerical The absorption correction (X-RED; Stoe & Cie, 2001) was performed after optimizing the crystal shape using X-SHAPE (Stoe & Cie, 1999). | k = −7→7 |
Tmin = 0.902, Tmax = 0.962 | l = −18→18 |
8608 measured reflections |
Refinement on F2 | Hydrogen site location: inferred from neighbouring sites |
Least-squares matrix: full | H atoms treated by a mixture of independent and constrained refinement |
R[F2 > 2σ(F2)] = 0.031 | w = 1/[σ2(Fo2) + (0.0526P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.084 | (Δ/σ)max = 0.001 |
S = 1.06 | Δρmax = 0.43 e Å−3 |
4004 reflections | Δρmin = −0.45 e Å−3 |
320 parameters | Extinction correction: SHELXL97 (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
29 restraints | Extinction coefficient: 0.081 (5) |
Primary atom site location: structure-invariant direct methods | Absolute structure: Flack (1983) |
Secondary atom site location: difference Fourier map | Absolute structure parameter: −0.02 (8) |
Experimental. A suitable single-crystal was carefully selected under a polarizing microscope and mounted in a glass capillary. The scattering intensities were collected on an imaging plate diffractometer (IPDS I, Stoe & Cie) equipped with a fine focus sealed tube X-ray source (Mo Kα, λ = 0.71073 Å) operating at 50 kV and 40 mA. Intensity data for the title compound were collected at room temperature by φ-scans in 100 frames (0 < φ < 200°, Δφ = 2°, exposure time of 5 min) in the 2 Θ range 3.8 to 56.3°. Structure solution and refinement were carried out using the programs SIR92 (Altomare et al., 1993) and SHELXL97 (Sheldrick, 1997). A numerical absorption correction (X-RED (Stoe & Cie, 2001) was applied after optimization of the crystal shape (X-SHAPE (Stoe & Cie, 1999)). The last cycles of refinement included atomic positions for all atoms, anisotropic parameters for all non-hydrogen atoms and isotropic thermal parameters for all hydrogen atoms. The final difference maps were free of any chemically significant features. The refinement was based on F2 for ALL reflections. |
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. |
x | y | z | Uiso*/Ueq | ||
P1 | 0.06286 (5) | 0.70682 (11) | 0.69882 (4) | 0.01697 (14) | |
P2 | 0.50392 (5) | 0.20332 (11) | 0.65964 (4) | 0.01664 (14) | |
P3 | 0.73850 (6) | 0.30542 (10) | 0.97653 (4) | 0.01667 (14) | |
O11 | 0.18639 (18) | 0.8277 (4) | 0.76074 (14) | 0.0335 (5) | |
H111 | 0.189 (4) | 0.847 (8) | 0.822 (3) | 0.066 (14)* | |
O12 | −0.06103 (17) | 0.7967 (4) | 0.72264 (14) | 0.0286 (4) | |
O13 | 0.06793 (16) | 0.7483 (3) | 0.59310 (12) | 0.0265 (5) | |
O14 | 0.07606 (18) | 0.4717 (3) | 0.72402 (14) | 0.0285 (4) | |
O21 | 0.49282 (19) | 0.3334 (4) | 0.75288 (15) | 0.0307 (5) | |
H211 | 0.548 (6) | 0.370 (11) | 0.790 (4) | 0.10 (2)* | |
O22 | 0.38360 (16) | 0.2665 (3) | 0.57963 (13) | 0.0274 (5) | |
O23 | 0.63168 (16) | 0.2661 (3) | 0.63262 (12) | 0.0240 (4) | |
O24 | 0.50188 (18) | −0.0326 (3) | 0.68323 (13) | 0.0268 (4) | |
O31 | 0.68406 (17) | 0.4504 (3) | 0.88660 (12) | 0.0240 (4) | |
O32 | 0.85225 (17) | 0.1739 (3) | 0.95559 (13) | 0.0269 (5) | |
O33 | 0.79062 (19) | 0.4514 (3) | 1.06460 (13) | 0.0277 (4) | |
O34 | 0.63092 (18) | 0.1584 (3) | 0.99590 (13) | 0.0272 (5) | |
N1 | 0.7063 (2) | 0.8299 (5) | 1.13488 (17) | 0.0273 (5) | |
H11 | 0.646 (3) | 0.805 (7) | 1.168 (2) | 0.049 (10)* | |
H12 | 0.716 (3) | 0.706 (4) | 1.106 (3) | 0.041 (9)* | |
H13 | 0.678 (3) | 0.929 (5) | 1.092 (2) | 0.037 (9)* | |
H14 | 0.777 (3) | 0.859 (7) | 1.181 (2) | 0.043 (10)* | |
N2 | 0.5190 (2) | −0.1752 (5) | 0.87680 (17) | 0.0292 (5) | |
H21 | 0.456 (3) | −0.215 (7) | 0.904 (2) | 0.048 (10)* | |
H22 | 0.485 (4) | −0.165 (7) | 0.8124 (15) | 0.051 (11)* | |
H23 | 0.572 (3) | −0.286 (4) | 0.882 (2) | 0.032 (8)* | |
H24 | 0.560 (4) | −0.070 (6) | 0.914 (3) | 0.059 (12)* | |
N3 | −0.1209 (2) | 0.2149 (5) | 0.76305 (15) | 0.0260 (4) | |
H31 | −0.201 (2) | 0.228 (7) | 0.724 (2) | 0.048 (10)* | |
H32 | −0.072 (3) | 0.325 (4) | 0.753 (2) | 0.025 (8)* | |
H33 | −0.125 (4) | 0.211 (8) | 0.8234 (15) | 0.052 (10)* | |
H34 | −0.094 (3) | 0.091 (4) | 0.749 (2) | 0.035 (9)* | |
N4 | 0.3232 (2) | −0.2974 (5) | 0.55885 (16) | 0.0260 (4) | |
H41 | 0.244 (2) | −0.278 (6) | 0.563 (2) | 0.034 (8)* | |
H42 | 0.346 (3) | −0.430 (3) | 0.576 (2) | 0.034 (9)* | |
H43 | 0.323 (3) | −0.278 (7) | 0.4968 (15) | 0.047 (10)* | |
H44 | 0.368 (3) | −0.203 (5) | 0.597 (2) | 0.038 (9)* | |
N5 | 0.1203 (2) | 0.1947 (5) | 0.57987 (15) | 0.0246 (4) | |
H51 | 0.2068 (18) | 0.196 (6) | 0.586 (2) | 0.029 (7)* | |
H52 | 0.106 (3) | 0.065 (3) | 0.596 (2) | 0.029 (9)* | |
H53 | 0.067 (2) | 0.219 (6) | 0.5208 (15) | 0.028 (7)* | |
H54 | 0.107 (3) | 0.282 (5) | 0.624 (2) | 0.034 (9)* | |
N6 | 0.32090 (19) | 0.2056 (5) | 0.37697 (16) | 0.0260 (4) | |
H61 | 0.2386 (19) | 0.230 (6) | 0.350 (2) | 0.028 (8)* | |
H62 | 0.337 (3) | 0.218 (7) | 0.4413 (14) | 0.036 (8)* | |
H63 | 0.339 (3) | 0.073 (3) | 0.367 (2) | 0.023 (8)* | |
H64 | 0.361 (4) | 0.289 (6) | 0.345 (3) | 0.055 (12)* | |
N7 | 0.9065 (2) | −0.2428 (4) | 0.91732 (19) | 0.0291 (6) | |
H71 | 0.975 (2) | −0.274 (7) | 0.9652 (19) | 0.039 (9)* | |
H72 | 0.879 (3) | −0.117 (4) | 0.934 (2) | 0.021 (8)* | |
H73 | 0.851 (3) | −0.337 (5) | 0.927 (3) | 0.050 (11)* | |
H74 | 0.926 (5) | −0.241 (9) | 0.859 (2) | 0.083 (16)* |
U11 | U22 | U33 | U12 | U13 | U23 | |
P1 | 0.0166 (2) | 0.0172 (3) | 0.0174 (3) | −0.0006 (3) | 0.00444 (18) | −0.0006 (3) |
P2 | 0.0159 (2) | 0.0166 (3) | 0.0175 (2) | 0.0001 (3) | 0.00408 (18) | −0.0003 (3) |
P3 | 0.0209 (3) | 0.0131 (3) | 0.0170 (3) | −0.0002 (2) | 0.0065 (2) | −0.0007 (2) |
O11 | 0.0271 (9) | 0.0465 (14) | 0.0268 (9) | −0.0146 (9) | 0.0061 (7) | −0.0087 (9) |
O12 | 0.0221 (8) | 0.0324 (12) | 0.0320 (9) | 0.0040 (8) | 0.0076 (7) | −0.0063 (8) |
O13 | 0.0263 (8) | 0.0341 (14) | 0.0188 (8) | −0.0024 (7) | 0.0047 (6) | 0.0021 (7) |
O14 | 0.0336 (9) | 0.0195 (12) | 0.0340 (10) | 0.0037 (7) | 0.0113 (8) | 0.0057 (8) |
O21 | 0.0224 (9) | 0.0415 (14) | 0.0282 (9) | −0.0007 (8) | 0.0059 (7) | −0.0149 (9) |
O22 | 0.0231 (8) | 0.0316 (14) | 0.0251 (9) | 0.0018 (7) | 0.0008 (6) | 0.0017 (7) |
O23 | 0.0196 (7) | 0.0274 (14) | 0.0259 (8) | −0.0012 (6) | 0.0072 (6) | 0.0006 (7) |
O24 | 0.0332 (9) | 0.0181 (11) | 0.0299 (10) | 0.0001 (7) | 0.0090 (7) | 0.0040 (8) |
O31 | 0.0297 (9) | 0.0196 (11) | 0.0213 (8) | −0.0029 (7) | 0.0032 (7) | 0.0029 (7) |
O32 | 0.0286 (8) | 0.0244 (13) | 0.0295 (9) | 0.0070 (7) | 0.0107 (7) | −0.0028 (8) |
O33 | 0.0386 (10) | 0.0225 (12) | 0.0205 (8) | 0.0005 (8) | 0.0045 (7) | −0.0047 (7) |
O34 | 0.0318 (9) | 0.0239 (13) | 0.0295 (9) | −0.0064 (7) | 0.0144 (7) | 0.0012 (7) |
N1 | 0.0307 (11) | 0.0232 (16) | 0.0283 (12) | −0.0002 (10) | 0.0075 (9) | 0.0011 (10) |
N2 | 0.0346 (12) | 0.0249 (16) | 0.0307 (12) | −0.0036 (10) | 0.0127 (9) | −0.0016 (11) |
N3 | 0.0274 (10) | 0.0254 (14) | 0.0278 (10) | 0.0013 (11) | 0.0114 (8) | 0.0007 (12) |
N4 | 0.0254 (10) | 0.0253 (14) | 0.0276 (10) | −0.0001 (11) | 0.0073 (8) | 0.0006 (12) |
N5 | 0.0262 (9) | 0.0231 (14) | 0.0244 (10) | 0.0002 (11) | 0.0060 (7) | 0.0020 (11) |
N6 | 0.0240 (10) | 0.0239 (14) | 0.0298 (11) | 0.0008 (11) | 0.0062 (8) | −0.0001 (12) |
N7 | 0.0259 (11) | 0.0241 (18) | 0.0398 (13) | −0.0015 (8) | 0.0129 (10) | 0.0026 (10) |
P1—O14 | 1.521 (2) | N2—H24 | 0.891 (19) |
P1—O12 | 1.5233 (18) | N3—H31 | 0.887 (18) |
P1—O13 | 1.5237 (17) | N3—H32 | 0.893 (18) |
P1—O11 | 1.573 (2) | N3—H33 | 0.859 (18) |
P2—O24 | 1.523 (2) | N3—H34 | 0.868 (19) |
P2—O23 | 1.5266 (17) | N4—H41 | 0.853 (18) |
P2—O22 | 1.5292 (18) | N4—H42 | 0.886 (19) |
P2—O21 | 1.574 (2) | N4—H43 | 0.882 (18) |
P3—O34 | 1.5312 (18) | N4—H44 | 0.861 (19) |
P3—O32 | 1.5352 (18) | N5—H51 | 0.888 (17) |
P3—O33 | 1.5356 (19) | N5—H52 | 0.876 (19) |
P3—O31 | 1.5548 (19) | N5—H53 | 0.896 (17) |
O11—H111 | 0.87 (4) | N5—H54 | 0.863 (18) |
O21—H211 | 0.72 (6) | N6—H61 | 0.868 (18) |
N1—H11 | 0.879 (19) | N6—H62 | 0.883 (18) |
N1—H12 | 0.899 (19) | N6—H63 | 0.873 (18) |
N1—H13 | 0.864 (19) | N6—H64 | 0.866 (19) |
N1—H14 | 0.882 (19) | N7—H71 | 0.884 (18) |
N2—H21 | 0.881 (18) | N7—H72 | 0.893 (18) |
N2—H22 | 0.894 (19) | N7—H73 | 0.864 (19) |
N2—H23 | 0.880 (18) | N7—H74 | 0.885 (19) |
O14—P1—O12 | 110.20 (12) | H23—N2—H24 | 109 (4) |
O14—P1—O13 | 111.85 (11) | H31—N3—H32 | 109 (3) |
O12—P1—O13 | 112.33 (11) | H31—N3—H33 | 111 (3) |
O14—P1—O11 | 108.96 (12) | H32—N3—H33 | 110 (4) |
O12—P1—O11 | 109.20 (12) | H31—N3—H34 | 105 (4) |
O13—P1—O11 | 104.07 (11) | H32—N3—H34 | 115 (3) |
O24—P2—O23 | 111.42 (11) | H33—N3—H34 | 106 (4) |
O24—P2—O22 | 111.24 (11) | H41—N4—H42 | 109 (3) |
O23—P2—O22 | 111.48 (10) | H41—N4—H43 | 106 (3) |
O24—P2—O21 | 108.55 (12) | H42—N4—H43 | 110 (4) |
O23—P2—O21 | 108.38 (11) | H41—N4—H44 | 105 (3) |
O22—P2—O21 | 105.51 (11) | H42—N4—H44 | 114 (3) |
O34—P3—O32 | 110.16 (11) | H43—N4—H44 | 113 (4) |
O34—P3—O33 | 110.71 (11) | H51—N5—H52 | 103 (3) |
O32—P3—O33 | 109.56 (11) | H51—N5—H53 | 119 (3) |
O34—P3—O31 | 110.92 (11) | H52—N5—H53 | 108 (3) |
O32—P3—O31 | 108.16 (11) | H51—N5—H54 | 105 (3) |
O33—P3—O31 | 107.24 (11) | H52—N5—H54 | 110 (3) |
P1—O11—H111 | 117 (3) | H53—N5—H54 | 112 (3) |
P2—O21—H211 | 125 (5) | H61—N6—H62 | 111 (3) |
H11—N1—H12 | 105 (4) | H61—N6—H63 | 109 (3) |
H11—N1—H13 | 108 (3) | H62—N6—H63 | 104 (3) |
H12—N1—H13 | 112 (3) | H61—N6—H64 | 103 (3) |
H11—N1—H14 | 103 (3) | H62—N6—H64 | 119 (4) |
H12—N1—H14 | 111 (4) | H63—N6—H64 | 110 (4) |
H13—N1—H14 | 117 (4) | H71—N7—H72 | 105 (3) |
H21—N2—H22 | 108 (3) | H71—N7—H73 | 101 (4) |
H21—N2—H23 | 105 (4) | H72—N7—H73 | 107 (3) |
H22—N2—H23 | 104 (4) | H71—N7—H74 | 113 (4) |
H21—N2—H24 | 105 (3) | H72—N7—H74 | 113 (4) |
H22—N2—H24 | 125 (4) | H73—N7—H74 | 118 (4) |
D—H···A | D—H | H···A | D···A | D—H···A |
O11—H111···O33i | 0.87 (4) | 1.69 (5) | 2.535 (3) | 164 (5) |
O21—H211···O31 | 0.72 (6) | 1.79 (6) | 2.510 (3) | 177 (8) |
N1—H11···O21i | 0.88 (2) | 2.04 (2) | 2.899 (3) | 165 (4) |
N1—H12···O33 | 0.90 (2) | 1.93 (2) | 2.802 (3) | 163 (3) |
N1—H13···O34ii | 0.86 (2) | 1.97 (2) | 2.828 (3) | 174 (3) |
N1—H14···O14i | 0.88 (2) | 1.92 (2) | 2.789 (3) | 170 (4) |
N2—H21···O34iii | 0.88 (2) | 2.01 (2) | 2.847 (3) | 159 (3) |
N2—H22···O24 | 0.89 (2) | 2.05 (3) | 2.833 (3) | 146 (4) |
N2—H23···O31iv | 0.88 (2) | 2.03 (2) | 2.907 (3) | 176 (3) |
N2—H24···O34 | 0.89 (2) | 1.88 (2) | 2.768 (3) | 174 (4) |
N3—H31···O23v | 0.89 (2) | 1.93 (2) | 2.814 (3) | 176 (4) |
N3—H32···O14 | 0.89 (2) | 1.93 (2) | 2.776 (3) | 158 (3) |
N3—H33···O32v | 0.86 (2) | 1.95 (2) | 2.801 (3) | 173 (4) |
N3—H34···O12iv | 0.87 (2) | 1.94 (2) | 2.797 (4) | 170 (3) |
N4—H41···O13iv | 0.85 (2) | 1.99 (2) | 2.840 (3) | 172 (3) |
N4—H42···O22iv | 0.89 (2) | 1.95 (2) | 2.818 (4) | 166 (3) |
N4—H43···O23vi | 0.88 (2) | 2.01 (2) | 2.872 (3) | 167 (3) |
N4—H44···O24 | 0.86 (2) | 1.94 (2) | 2.791 (3) | 167 (4) |
N5—H51···O22 | 0.89 (2) | 1.93 (2) | 2.794 (3) | 165 (3) |
N5—H52···O13iv | 0.88 (2) | 2.03 (2) | 2.879 (4) | 163 (3) |
N5—H53···O13vii | 0.90 (2) | 1.88 (2) | 2.764 (3) | 169 (3) |
N5—H54···O14 | 0.86 (2) | 1.93 (2) | 2.796 (3) | 178 (4) |
N6—H61···O12vii | 0.87 (2) | 1.94 (2) | 2.807 (3) | 173 (3) |
N6—H62···O22 | 0.88 (2) | 1.92 (2) | 2.797 (3) | 174 (4) |
N6—H63···O23vi | 0.87 (2) | 1.96 (2) | 2.821 (4) | 169 (3) |
N6—H64···O24viii | 0.87 (2) | 1.93 (2) | 2.761 (3) | 160 (4) |
N7—H71···O32ix | 0.88 (2) | 1.91 (2) | 2.776 (3) | 166 (3) |
N7—H72···O32 | 0.89 (2) | 1.89 (2) | 2.765 (3) | 166 (3) |
N7—H73···O31iv | 0.86 (2) | 2.17 (2) | 2.977 (3) | 156 (3) |
N7—H73···O33iv | 0.86 (2) | 2.55 (3) | 3.266 (3) | 141 (3) |
N7—H74···O12x | 0.89 (2) | 1.97 (2) | 2.850 (3) | 169 (5) |
Symmetry codes: (i) −x+1, y+1/2, −z+2; (ii) x, y+1, z; (iii) −x+1, y−1/2, −z+2; (iv) x, y−1, z; (v) x−1, y, z; (vi) −x+1, y−1/2, −z+1; (vii) −x, y−1/2, −z+1; (viii) −x+1, y+1/2, −z+1; (ix) −x+2, y−1/2, −z+2; (x) x+1, y−1, z. |
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