In the title compound, [Fe(H2O)6](NO3)2·2C6H12N4·4H2O, the ferrous ion is coordinated by six O atoms from six water molecules and is in a slightly distorted octahedral geometry, lying on an inversion center. All the N atoms of the hexamethylenetetramine molecules, all the O atoms in the nitrate anions and all the water molecules contribute to the formation of hydrogen bonds. This leads to the formation of a three-dimensional network.
Supporting information
CCDC reference: 226656
Key indicators
- Single-crystal X-ray study
- T = 298 K
- Mean (O-N) = 0.005 Å
- R factor = 0.043
- wR factor = 0.117
- Data-to-parameter ratio = 9.2
checkCIF/PLATON results
No syntax errors found
Alert level B
PLAT029_ALERT_3_B _diffrn_measured_fraction_theta_full Low ....... 0.99
PLAT242_ALERT_2_B Check Low U(eq) as Compared to Neighbors .... N1
PLAT731_ALERT_1_B Bond Calc 0.91(7), Rep 0.906(11) ...... 6.36 su-Rat
O8 -H10 1.555 1.555
PLAT735_ALERT_1_B D-H Calc 0.91(7), Rep 0.906(11) ...... 6.36 su-Rat
O8 -H10 1.555 1.555
Alert level C
REFNR01_ALERT_3_C Ratio of reflections to parameters is < 10 for a
centrosymmetric structure
sine(theta)/lambda -0.1443
Proportion of unique data used 1.0000
Ratio reflections to parameters 9.1579
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT088_ALERT_3_C Poor Data / Parameter Ratio .................... 9.16
PLAT164_ALERT_4_C Nr. of Refined C-H H-Atoms in Heavy-At Struct... 12
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Fe1 - O1 = 9.53 su
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Fe1 - O2 = 7.87 su
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Fe1 - O3 = 7.76 su
PLAT242_ALERT_2_C Check Low U(eq) as Compared to Neighbors .... Fe1
PLAT417_ALERT_2_C Short Inter D-H..H-D H8 .. H10 = 2.14 Ang.
PLAT731_ALERT_1_C Bond Calc 0.90(3), Rep 0.904(10) ...... 3.00 su-Rat
O1 -H2 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.91(3), Rep 0.905(10) ...... 3.00 su-Rat
O2 -H3 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.90(4), Rep 0.903(10) ...... 4.00 su-Rat
O2 -H4 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.91(3), Rep 0.911(10) ...... 3.00 su-Rat
O3 -H5 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.91(4), Rep 0.907(10) ...... 4.00 su-Rat
O7 -H8 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.91(4), Rep 0.912(10) ...... 4.00 su-Rat
O8 -H9 1.555 1.555
PLAT732_ALERT_1_C Angle Calc 106(5), Rep 106(2) ...... 2.50 su-Rat
H9 -O8 -H10 1.555 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.90(3), Rep 0.904(10) ...... 3.00 su-Rat
O1 -H2 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.91(3), Rep 0.905(10) ...... 3.00 su-Rat
O2 -H3 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.90(4), Rep 0.903(10) ...... 4.00 su-Rat
O2 -H4 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.91(3), Rep 0.911(10) ...... 3.00 su-Rat
O3 -H5 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.91(4), Rep 0.907(10) ...... 4.00 su-Rat
O7 -H8 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.91(4), Rep 0.912(10) ...... 4.00 su-Rat
O8 -H9 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.91(4), Rep 1.908(13) ...... 3.08 su-Rat
H4 -N2 1.555 1.554
PLAT736_ALERT_1_C H...A Calc 1.96(4), Rep 1.965(15) ...... 2.67 su-Rat
H5 -O6 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.92(4), Rep 1.917(12) ...... 3.33 su-Rat
H8 -O8 1.555 2.666
PLAT736_ALERT_1_C H...A Calc 1.89(4), Rep 1.887(15) ...... 2.67 su-Rat
H9 -O5 1.555 1.655
PLAT736_ALERT_1_C H...A Calc 2.03(7), Rep 2.02(2) ...... 3.50 su-Rat
H10 -O6 1.555 2.666
0 ALERT level A = In general: serious problem
4 ALERT level B = Potentially serious problem
27 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
21 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
6 ALERT type 2 Indicator that the structure model may be wrong or deficient
3 ALERT type 3 Indicator that the structure quality may be low
1 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: SMART (Siemens, 1996); cell refinement: SMART; data reduction: SAINT (Siemens, 1996); program(s) used to solve structure: SHELXTL (Sheldrick, 1997); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.
Hexaquairon(II) dinitrate bis(dihexamethylenetetramine) tetrahydrate
top
Crystal data top
[Fe(H2O)6](NO3)2·2C6H12N4·4H2O | Z = 1 |
Mr = 640.42 | F(000) = 340 |
Triclinic, P1 | Dx = 1.523 Mg m−3 |
Hall symbol: -P 1 | Mo Kα radiation, λ = 0.71073 Å |
a = 9.104 (4) Å | Cell parameters from 2715 reflections |
b = 9.349 (4) Å | θ = 3.0–26.4° |
c = 9.700 (4) Å | µ = 0.63 mm−1 |
α = 87.743 (5)° | T = 298 K |
β = 75.674 (4)° | Prism, violet |
γ = 61.248 (5)° | 0.33 × 0.25 × 0.18 mm |
V = 698.3 (5) Å3 | |
Data collection top
Siemens SMART CCD area-detector diffractometer | 2436 independent reflections |
Radiation source: fine-focus sealed tube | 2261 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.015 |
φ and ω scans | θmax = 25.0°, θmin = 2.2° |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | h = −10→9 |
Tmin = 0.820, Tmax = 0.896 | k = −10→11 |
3689 measured reflections | l = −11→11 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.043 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.117 | All H-atom parameters refined |
S = 1.09 | w = 1/[σ2(Fo2) + (0.0803P)2 + 0.1663P] where P = (Fo2 + 2Fc2)/3 |
2436 reflections | (Δ/σ)max = 0.001 |
266 parameters | Δρmax = 0.63 e Å−3 |
15 restraints | Δρmin = −0.46 e Å−3 |
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 | x | y | z | Uiso*/Ueq | |
Fe1 | 0.0000 | 0.0000 | 0.0000 | 0.02441 (18) | |
N1 | 0.0679 (3) | 0.1779 (4) | 0.4947 (3) | 0.0569 (7) | |
N2 | 0.3474 (3) | 0.1892 (3) | 0.8379 (3) | 0.0436 (5) | |
N3 | 0.4508 (3) | 0.2981 (3) | 0.6246 (2) | 0.0448 (5) | |
N4 | 0.5474 (3) | 0.2929 (3) | 0.8398 (2) | 0.0411 (5) | |
N5 | 0.2472 (3) | 0.4831 (3) | 0.8372 (2) | 0.0418 (5) | |
O1 | 0.1077 (2) | −0.1802 (2) | 0.1308 (2) | 0.0432 (4) | |
O2 | 0.2427 (2) | −0.0491 (2) | −0.1071 (2) | 0.0428 (4) | |
O3 | −0.0082 (3) | 0.1771 (2) | 0.1272 (2) | 0.0458 (5) | |
O4 | 0.1005 (5) | 0.0737 (5) | 0.5792 (3) | 0.0997 (10) | |
O5 | −0.0261 (6) | 0.3204 (4) | 0.5399 (5) | 0.1432 (17) | |
O6 | 0.1350 (4) | 0.1425 (4) | 0.3645 (3) | 0.0783 (8) | |
O7 | 0.5191 (3) | 0.2702 (3) | 0.3233 (2) | 0.0647 (6) | |
O8 | 0.8043 (4) | 0.5914 (4) | 0.7424 (3) | 0.0804 (8) | |
C1 | 0.4008 (4) | 0.1742 (4) | 0.6798 (3) | 0.0492 (7) | |
C2 | 0.4944 (4) | 0.1694 (4) | 0.8904 (3) | 0.0454 (6) | |
C3 | 0.2006 (4) | 0.3560 (4) | 0.8881 (3) | 0.0443 (6) | |
C4 | 0.5952 (4) | 0.2769 (4) | 0.6819 (3) | 0.0450 (6) | |
C5 | 0.3028 (4) | 0.4614 (4) | 0.6790 (3) | 0.0464 (6) | |
C6 | 0.3967 (4) | 0.4562 (3) | 0.8908 (3) | 0.0421 (6) | |
H1 | 0.053 (4) | −0.162 (5) | 0.2254 (14) | 0.072 (11)* | |
H2 | 0.2226 (15) | −0.225 (5) | 0.123 (3) | 0.078 (12)* | |
H3 | 0.309 (5) | −0.122 (4) | −0.185 (3) | 0.089 (13)* | |
H4 | 0.265 (5) | 0.035 (3) | −0.119 (4) | 0.097 (15)* | |
H5 | 0.024 (5) | 0.157 (4) | 0.211 (2) | 0.066 (10)* | |
H6 | −0.073 (4) | 0.2884 (14) | 0.131 (3) | 0.072 (11)* | |
H7 | 0.503 (4) | 0.273 (5) | 0.4195 (12) | 0.071 (11)* | |
H8 | 0.413 (3) | 0.322 (5) | 0.306 (4) | 0.087 (14)* | |
H9 | 0.857 (7) | 0.497 (4) | 0.684 (5) | 0.117 (19)* | |
H10 | 0.831 (11) | 0.662 (6) | 0.690 (6) | 0.23 (4)* | |
H11 | 0.309 (4) | 0.178 (4) | 0.638 (3) | 0.050 (8)* | |
H12 | 0.498 (5) | 0.061 (5) | 0.638 (4) | 0.057 (9)* | |
H13 | 0.454 (4) | 0.188 (4) | 1.008 (3) | 0.051 (8)* | |
H14 | 0.601 (5) | 0.046 (5) | 0.850 (4) | 0.061 (9)* | |
H15 | 0.167 (4) | 0.366 (4) | 0.999 (4) | 0.049 (8)* | |
H16 | 0.097 (4) | 0.374 (3) | 0.851 (3) | 0.039 (7)* | |
H17 | 0.697 (4) | 0.167 (4) | 0.651 (3) | 0.049 (8)* | |
H18 | 0.620 (4) | 0.373 (4) | 0.650 (3) | 0.048 (8)* | |
H19 | 0.205 (5) | 0.479 (5) | 0.635 (4) | 0.065 (10)* | |
H20 | 0.328 (4) | 0.551 (4) | 0.644 (3) | 0.052 (8)* | |
H21 | 0.356 (4) | 0.463 (3) | 1.002 (3) | 0.041 (7)* | |
H22 | 0.425 (4) | 0.540 (4) | 0.861 (3) | 0.048 (8)* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Fe1 | 0.0236 (3) | 0.0241 (3) | 0.0244 (3) | −0.01027 (19) | −0.00718 (17) | 0.00218 (17) |
N1 | 0.0503 (15) | 0.0641 (18) | 0.0500 (15) | −0.0221 (13) | −0.0139 (12) | −0.0010 (13) |
N2 | 0.0418 (12) | 0.0410 (12) | 0.0501 (13) | −0.0227 (10) | −0.0098 (10) | 0.0016 (10) |
N3 | 0.0449 (13) | 0.0502 (14) | 0.0376 (12) | −0.0216 (11) | −0.0102 (10) | −0.0012 (10) |
N4 | 0.0379 (11) | 0.0438 (12) | 0.0450 (12) | −0.0203 (10) | −0.0160 (9) | 0.0071 (10) |
N5 | 0.0401 (12) | 0.0377 (12) | 0.0429 (12) | −0.0141 (10) | −0.0129 (9) | 0.0009 (9) |
O1 | 0.0395 (10) | 0.0471 (11) | 0.0424 (10) | −0.0190 (9) | −0.0157 (8) | 0.0123 (8) |
O2 | 0.0369 (10) | 0.0419 (11) | 0.0454 (11) | −0.0197 (8) | −0.0019 (8) | −0.0020 (8) |
O3 | 0.0535 (12) | 0.0360 (10) | 0.0465 (11) | −0.0161 (9) | −0.0222 (9) | −0.0007 (8) |
O4 | 0.117 (3) | 0.106 (2) | 0.0615 (17) | −0.043 (2) | −0.0243 (17) | 0.0243 (17) |
O5 | 0.150 (4) | 0.069 (2) | 0.128 (3) | −0.009 (2) | 0.010 (3) | −0.023 (2) |
O6 | 0.0853 (18) | 0.095 (2) | 0.0471 (13) | −0.0388 (16) | −0.0160 (12) | 0.0033 (13) |
O7 | 0.0604 (15) | 0.0710 (16) | 0.0436 (12) | −0.0231 (12) | 0.0002 (10) | −0.0054 (11) |
O8 | 0.0822 (19) | 0.082 (2) | 0.0692 (17) | −0.0351 (17) | −0.0173 (14) | 0.0053 (15) |
C1 | 0.0513 (17) | 0.0489 (17) | 0.0498 (16) | −0.0270 (14) | −0.0096 (13) | −0.0082 (13) |
C2 | 0.0439 (15) | 0.0406 (15) | 0.0511 (16) | −0.0189 (12) | −0.0164 (12) | 0.0109 (12) |
C3 | 0.0352 (14) | 0.0470 (16) | 0.0488 (16) | −0.0196 (12) | −0.0080 (12) | −0.0011 (12) |
C4 | 0.0377 (15) | 0.0507 (17) | 0.0451 (15) | −0.0218 (13) | −0.0074 (12) | 0.0034 (12) |
C5 | 0.0466 (16) | 0.0480 (16) | 0.0440 (15) | −0.0195 (13) | −0.0191 (12) | 0.0092 (12) |
C6 | 0.0466 (15) | 0.0410 (15) | 0.0444 (15) | −0.0232 (12) | −0.0167 (12) | 0.0022 (11) |
Geometric parameters (Å, º) top
Fe1—O2i | 2.0242 (19) | O1—H2 | 0.904 (10) |
Fe1—O2 | 2.0242 (19) | O2—H3 | 0.905 (10) |
Fe1—O3 | 2.0658 (19) | O2—H4 | 0.903 (10) |
Fe1—O3i | 2.0658 (19) | O3—H5 | 0.911 (10) |
Fe1—O1i | 2.0660 (18) | O3—H6 | 0.913 (10) |
Fe1—O1 | 2.0660 (18) | O7—H7 | 0.906 (10) |
N1—O5 | 1.209 (4) | O7—H8 | 0.907 (10) |
N1—O4 | 1.220 (4) | O8—H9 | 0.912 (10) |
N1—O6 | 1.238 (4) | O8—H10 | 0.906 (11) |
N2—C2 | 1.474 (4) | C1—H11 | 1.00 (3) |
N2—C3 | 1.479 (4) | C1—H12 | 1.01 (4) |
N2—C1 | 1.480 (4) | C2—H13 | 1.10 (3) |
N3—C5 | 1.469 (4) | C2—H14 | 1.09 (4) |
N3—C1 | 1.474 (4) | C3—H15 | 1.04 (3) |
N3—C4 | 1.476 (4) | C3—H16 | 1.03 (3) |
N4—C6 | 1.472 (4) | C4—H17 | 0.98 (3) |
N4—C2 | 1.477 (4) | C4—H18 | 1.05 (3) |
N4—C4 | 1.478 (4) | C5—H19 | 1.02 (4) |
N5—C3 | 1.473 (4) | C5—H20 | 1.00 (4) |
N5—C5 | 1.481 (4) | C6—H21 | 1.04 (3) |
N5—C6 | 1.482 (3) | C6—H22 | 0.95 (3) |
O1—H1 | 0.907 (10) | | |
| | | |
O2i—Fe1—O2 | 180.00 (10) | H7—O7—H8 | 107 (2) |
O2i—Fe1—O3 | 92.38 (8) | H9—O8—H10 | 106 (2) |
O2—Fe1—O3 | 87.62 (8) | N3—C1—N2 | 112.0 (2) |
O2i—Fe1—O3i | 87.62 (8) | N3—C1—H11 | 111.2 (19) |
O2—Fe1—O3i | 92.38 (8) | N2—C1—H11 | 111.4 (18) |
O3—Fe1—O3i | 180.00 (11) | N3—C1—H12 | 110 (2) |
O2i—Fe1—O1i | 88.59 (8) | N2—C1—H12 | 112.7 (19) |
O2—Fe1—O1i | 91.41 (8) | H11—C1—H12 | 99 (3) |
O3—Fe1—O1i | 87.60 (8) | N2—C2—N4 | 111.7 (2) |
O3i—Fe1—O1i | 92.40 (8) | N2—C2—H13 | 109.1 (16) |
O2i—Fe1—O1 | 91.41 (8) | N4—C2—H13 | 106.5 (17) |
O2—Fe1—O1 | 88.59 (8) | N2—C2—H14 | 106.4 (18) |
O3—Fe1—O1 | 92.40 (8) | N4—C2—H14 | 110.4 (19) |
O3i—Fe1—O1 | 87.60 (8) | H13—C2—H14 | 113 (2) |
O1i—Fe1—O1 | 180.0 | N5—C3—N2 | 111.7 (2) |
O5—N1—O4 | 119.0 (4) | N5—C3—H15 | 109.4 (18) |
O5—N1—O6 | 119.1 (4) | N2—C3—H15 | 107.5 (18) |
O4—N1—O6 | 121.8 (3) | N5—C3—H16 | 107.7 (16) |
C2—N2—C3 | 108.3 (2) | N2—C3—H16 | 110.0 (16) |
C2—N2—C1 | 108.0 (2) | H15—C3—H16 | 111 (2) |
C3—N2—C1 | 108.4 (2) | N3—C4—N4 | 111.9 (2) |
C5—N3—C1 | 108.5 (2) | N3—C4—H17 | 111.1 (19) |
C5—N3—C4 | 108.0 (2) | N4—C4—H17 | 106.7 (18) |
C1—N3—C4 | 108.2 (2) | N3—C4—H18 | 106.6 (17) |
C6—N4—C2 | 107.9 (2) | N4—C4—H18 | 106.7 (17) |
C6—N4—C4 | 108.4 (2) | H17—C4—H18 | 114 (3) |
C2—N4—C4 | 108.5 (2) | N3—C5—N5 | 112.1 (2) |
C3—N5—C5 | 108.4 (2) | N3—C5—H19 | 108 (2) |
C3—N5—C6 | 107.7 (2) | N5—C5—H19 | 112 (2) |
C5—N5—C6 | 108.4 (2) | N3—C5—H20 | 112.3 (19) |
Fe1—O1—H1 | 118 (2) | N5—C5—H20 | 108.6 (18) |
Fe1—O1—H2 | 118 (2) | H19—C5—H20 | 103 (3) |
H1—O1—H2 | 107 (2) | N4—C6—N5 | 111.8 (2) |
Fe1—O2—H3 | 125 (3) | N4—C6—H21 | 108.1 (16) |
Fe1—O2—H4 | 118 (3) | N5—C6—H21 | 106.3 (16) |
H3—O2—H4 | 107 (2) | N4—C6—H22 | 111.2 (19) |
Fe1—O3—H5 | 123 (2) | N5—C6—H22 | 108.2 (19) |
Fe1—O3—H6 | 129 (2) | H21—C6—H22 | 111 (2) |
H5—O3—H6 | 105 (2) | | |
| | | |
C5—N3—C1—N2 | −58.2 (3) | C5—N3—C4—N4 | 59.0 (3) |
C4—N3—C1—N2 | 58.8 (3) | C1—N3—C4—N4 | −58.2 (3) |
C2—N2—C1—N3 | −59.1 (3) | C6—N4—C4—N3 | −58.8 (3) |
C3—N2—C1—N3 | 58.1 (3) | C2—N4—C4—N3 | 58.1 (3) |
C3—N2—C2—N4 | −58.6 (3) | C1—N3—C5—N5 | 58.3 (3) |
C1—N2—C2—N4 | 58.7 (3) | C4—N3—C5—N5 | −58.8 (3) |
C6—N4—C2—N2 | 58.9 (3) | C3—N5—C5—N3 | −58.5 (3) |
C4—N4—C2—N2 | −58.4 (3) | C6—N5—C5—N3 | 58.2 (3) |
C5—N5—C3—N2 | 58.3 (3) | C2—N4—C6—N5 | −59.4 (3) |
C6—N5—C3—N2 | −58.9 (3) | C4—N4—C6—N5 | 58.0 (3) |
C2—N2—C3—N5 | 58.8 (3) | C3—N5—C6—N4 | 59.5 (3) |
C1—N2—C3—N5 | −58.2 (3) | C5—N5—C6—N4 | −57.7 (3) |
Symmetry code: (i) −x, −y, −z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···O4ii | 0.91 (1) | 1.98 (1) | 2.874 (4) | 167 (3) |
O1—H2···N4iii | 0.90 (1) | 2.00 (2) | 2.879 (3) | 165 (3) |
O2—H3···O7iv | 0.91 (1) | 1.79 (2) | 2.674 (3) | 167 (4) |
O2—H4···N2v | 0.90 (1) | 1.91 (1) | 2.803 (3) | 171 (4) |
O3—H5···O6 | 0.91 (1) | 1.97 (2) | 2.850 (3) | 163 (3) |
O3—H6···N5vi | 0.91 (1) | 1.93 (1) | 2.830 (3) | 168 (4) |
O7—H7···N3 | 0.91 (1) | 1.92 (1) | 2.828 (3) | 175 (3) |
O7—H8···O8vii | 0.91 (1) | 1.92 (1) | 2.819 (4) | 174 (4) |
O8—H9···O5viii | 0.91 (1) | 1.89 (2) | 2.791 (5) | 171 (5) |
O8—H10···O6vii | 0.91 (1) | 2.02 (2) | 2.899 (5) | 162 (6) |
Symmetry codes: (ii) −x, −y, −z+1; (iii) −x+1, −y, −z+1; (iv) −x+1, −y, −z; (v) x, y, z−1; (vi) −x, −y+1, −z+1; (vii) −x+1, −y+1, −z+1; (viii) x+1, y, z. |