catena-Poly[[[diaqua­(1,10-phenanthroline-κ²N,N′)nickel(II)]-μ-4-carboxyl­atophenoxy­acetato-κ²O:O′] monohydrate]

In the title coordination polymer, {[Ni(4-CPOA)(phen)(H₂O)₂]·H₂O}_n (phen is 1,10-phenanthroline, C₁₂H₈N₂; 4-CPOA is the 4-carboxy­phenoxy­acetate dianion, C₉H₆O₅), each Ni^II ion displays a distorted octa­hedral geometry, defined by two carboxyl O atoms from two different 4-CPOA ligands, two N atoms from one phen mol­ecule and two coordinated water mol­ecules. The Ni^II ions are bridged by carboxyl­ate groups of 4-CPOA to form a chain structure. Adjacent polymeric chains are connected via hydrogen bonds and π–π stacking to construct a three-dimensional supramolecular network.

Key indicators

• Single-crystal X-ray study
• T = 295 K
• Mean [sigma](C-C) = 0.003 Å
• R factor = 0.033
• wR factor = 0.082
• Data-to-parameter ratio = 14.7

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........          6

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   1 ALERT level C = Check and explain
   0 ALERT level G = General alerts; check

   0 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
   0 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion

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Computing details

Data collection: RAPID-AUTO (Rigaku, 1998); cell refinement: RAPID-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPII (Johnson, 1976); software used to prepare material for publication: SHELXL97.

catena-Poly[[[diaqua(1,10-phenanthroline-κ²N,N')nickel(II)]- µ-4-carboxylatophenoxyacetato-κ²O:O'] monohydrate]

Crystal data

[Ni(C9H6O5)(C12H8N2)(H2O)2]·H2O	F(000) = 1008
Mr = 487.08	Dx = 1.634 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 8221 reflections
a = 6.8077 (14) Å	θ = 3.0–27.5°
b = 10.725 (2) Å	µ = 1.04 mm^−1
c = 27.313 (6) Å	T = 295 K
β = 96.76 (3)°	Prism, green
V = 1980.3 (7) Å^3	0.36 × 0.25 × 0.18 mm
Z = 4

Data collection

Rigaku R-AXIS RAPID diffractometer	4528 independent reflections
Radiation source: fine-focus sealed tube	3552 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.017
Detector resolution: 10.00 pixels mm^-1	θmax = 27.5°, θmin = 3.0°
ω scans	h = −8→8
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	k = −13→13
Tmin = 0.707, Tmax = 0.835	l = −35→35
8696 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.033	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.082	H atoms treated by a mixture of independent and constrained refinement
S = 1.03	w = 1/[σ^2(Fo^2) + (0.048P)^2] where P = (Fo^2 + 2Fc^2)/3
4528 reflections	(Δ/σ)max = 0.002
307 parameters	Δρmax = 0.38 e Å^−3
9 restraints	Δρmin = −0.27 e Å^−3

Special details

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ni1	0.40077 (3)	0.55288 (2)	0.624962 (8)	0.02889 (8)
O1W	0.6128 (2)	0.57182 (13)	0.57751 (5)	0.0381 (3)
H1W1	0.577 (3)	0.6143 (19)	0.5513 (6)	0.057*
H1W2	0.721 (2)	0.602 (2)	0.5913 (7)	0.057*
O2W	0.1832 (2)	0.52520 (13)	0.67435 (5)	0.0368 (3)
H2W1	0.145 (3)	0.4554 (11)	0.6613 (8)	0.055*
H2W2	0.106 (3)	0.5806 (14)	0.6594 (8)	0.055*
O3W	0.5337 (2)	0.68922 (17)	0.48969 (6)	0.0512 (4)
H3W1	0.4129 (18)	0.706 (2)	0.4816 (9)	0.077*
H3W2	0.577 (3)	0.641 (2)	0.4691 (8)	0.077*
O1	0.2400 (2)	0.45074 (12)	0.57128 (5)	0.0372 (3)
O2	0.0519 (2)	0.33772 (13)	0.61654 (5)	0.0460 (4)
O3	−0.1452 (2)	0.23046 (12)	0.53589 (5)	0.0398 (3)
O4	0.27128 (19)	−0.28304 (12)	0.60043 (5)	0.0363 (3)
O5	−0.0357 (2)	−0.31731 (13)	0.61806 (6)	0.0443 (4)
C1	0.1014 (3)	0.37404 (17)	0.57728 (7)	0.0332 (4)
C2	−0.0067 (3)	0.32660 (17)	0.52893 (7)	0.0372 (5)
H2A	−0.0759	0.3956	0.5116	0.045*
H2B	0.0894	0.2951	0.5085	0.045*
C3	−0.0754 (3)	0.11548 (16)	0.55165 (7)	0.0332 (4)
C4	0.1214 (3)	0.08004 (17)	0.55450 (8)	0.0356 (4)
H4	0.2173	0.1358	0.5465	0.043*
C5	0.1723 (3)	−0.04018 (17)	0.56951 (7)	0.0351 (4)
H5	0.3038	−0.0649	0.5711	0.042*
C6	0.0337 (3)	−0.12459 (16)	0.58221 (7)	0.0309 (4)
C7	−0.1631 (3)	−0.08685 (18)	0.57897 (8)	0.0366 (4)
H7	−0.2589	−0.1422	0.5874	0.044*
C8	−0.2172 (3)	0.03204 (18)	0.56338 (8)	0.0385 (5)
H8	−0.3493	0.0560	0.5608	0.046*
C9	0.0934 (3)	−0.25143 (17)	0.60100 (7)	0.0317 (4)
N2	0.5556 (2)	0.40101 (15)	0.65911 (6)	0.0324 (3)
N1	0.5744 (2)	0.64317 (15)	0.68166 (6)	0.0322 (3)
C10	0.5892 (3)	0.76409 (18)	0.69113 (8)	0.0377 (4)
H10	0.5300	0.8200	0.6679	0.045*
C11	0.6909 (3)	0.8112 (2)	0.73489 (8)	0.0437 (5)
H11	0.7001	0.8968	0.7401	0.052*
C12	0.7755 (3)	0.7308 (2)	0.76947 (8)	0.0444 (5)
H12	0.8385	0.7610	0.7992	0.053*
C13	0.7679 (3)	0.6024 (2)	0.76032 (7)	0.0378 (5)
C14	0.8568 (3)	0.5105 (2)	0.79387 (8)	0.0456 (5)
H14	0.9203	0.5356	0.8243	0.055*
C15	0.8504 (3)	0.3881 (2)	0.78222 (8)	0.0436 (5)
H15	0.9105	0.3305	0.8046	0.052*
C16	0.7528 (3)	0.3457 (2)	0.73596 (7)	0.0373 (4)
C17	0.7415 (3)	0.2199 (2)	0.72176 (8)	0.0419 (5)
H17	0.7992	0.1585	0.7428	0.050*
C18	0.6453 (3)	0.1888 (2)	0.67700 (8)	0.0451 (5)
H18	0.6412	0.1062	0.6666	0.054*
C19	0.5528 (3)	0.28166 (19)	0.64668 (8)	0.0396 (5)
H19	0.4861	0.2586	0.6164	0.048*
C20	0.6584 (3)	0.43341 (18)	0.70285 (7)	0.0320 (4)
C21	0.6665 (3)	0.56290 (18)	0.71523 (7)	0.0312 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ni1	0.03072 (14)	0.02585 (12)	0.02898 (13)	−0.00082 (10)	−0.00113 (9)	0.00096 (9)
O1W	0.0331 (8)	0.0446 (8)	0.0359 (7)	−0.0031 (6)	0.0009 (6)	0.0032 (6)
O2W	0.0415 (8)	0.0342 (7)	0.0341 (7)	−0.0006 (6)	0.0014 (6)	0.0024 (6)
O3W	0.0432 (9)	0.0638 (11)	0.0468 (9)	0.0114 (8)	0.0056 (7)	0.0018 (8)
O1	0.0380 (8)	0.0374 (7)	0.0353 (7)	−0.0081 (6)	0.0006 (6)	−0.0036 (6)
O2	0.0586 (10)	0.0390 (8)	0.0402 (8)	−0.0136 (7)	0.0052 (7)	0.0006 (7)
O3	0.0345 (7)	0.0251 (6)	0.0563 (9)	−0.0012 (6)	−0.0088 (7)	0.0035 (6)
O4	0.0335 (7)	0.0311 (7)	0.0436 (8)	0.0025 (6)	0.0013 (6)	0.0071 (6)
O5	0.0354 (8)	0.0388 (8)	0.0574 (9)	−0.0048 (6)	0.0000 (7)	0.0150 (7)
C1	0.0332 (10)	0.0257 (9)	0.0394 (11)	0.0016 (8)	−0.0016 (8)	−0.0001 (8)
C2	0.0394 (11)	0.0285 (9)	0.0409 (11)	−0.0058 (8)	−0.0074 (9)	0.0029 (8)
C3	0.0366 (10)	0.0254 (9)	0.0356 (10)	0.0003 (8)	−0.0044 (8)	−0.0013 (7)
C4	0.0333 (10)	0.0288 (9)	0.0433 (11)	−0.0041 (8)	−0.0008 (8)	−0.0005 (8)
C5	0.0312 (10)	0.0341 (10)	0.0384 (10)	0.0016 (8)	−0.0018 (8)	0.0009 (8)
C6	0.0318 (10)	0.0287 (9)	0.0310 (9)	0.0006 (8)	−0.0011 (8)	−0.0005 (7)
C7	0.0346 (11)	0.0302 (9)	0.0449 (11)	−0.0025 (8)	0.0040 (9)	0.0026 (8)
C8	0.0299 (10)	0.0337 (10)	0.0510 (12)	0.0013 (8)	0.0012 (9)	−0.0008 (9)
C9	0.0351 (10)	0.0294 (9)	0.0287 (9)	−0.0034 (8)	−0.0037 (8)	−0.0022 (7)
N2	0.0345 (9)	0.0319 (8)	0.0297 (8)	0.0002 (7)	−0.0005 (7)	0.0010 (6)
N1	0.0307 (8)	0.0315 (8)	0.0344 (8)	0.0006 (7)	0.0038 (7)	−0.0026 (7)
C10	0.0359 (11)	0.0329 (10)	0.0448 (11)	−0.0023 (8)	0.0073 (9)	−0.0020 (9)
C11	0.0372 (12)	0.0416 (11)	0.0531 (13)	−0.0080 (9)	0.0092 (10)	−0.0167 (10)
C12	0.0339 (11)	0.0581 (13)	0.0411 (11)	−0.0075 (10)	0.0036 (9)	−0.0172 (10)
C13	0.0290 (10)	0.0514 (12)	0.0329 (10)	−0.0031 (9)	0.0028 (8)	−0.0048 (9)
C14	0.0357 (11)	0.0709 (15)	0.0287 (10)	−0.0014 (11)	−0.0027 (9)	−0.0005 (10)
C15	0.0356 (11)	0.0603 (14)	0.0339 (11)	0.0057 (10)	−0.0001 (9)	0.0112 (10)
C16	0.0291 (10)	0.0477 (12)	0.0354 (10)	0.0055 (9)	0.0045 (8)	0.0092 (9)
C17	0.0361 (11)	0.0413 (11)	0.0483 (12)	0.0114 (9)	0.0046 (9)	0.0144 (9)
C18	0.0504 (13)	0.0331 (10)	0.0527 (13)	0.0083 (9)	0.0099 (11)	0.0020 (9)
C19	0.0455 (12)	0.0342 (10)	0.0387 (11)	0.0029 (9)	0.0032 (9)	−0.0003 (9)
C20	0.0283 (9)	0.0357 (10)	0.0323 (9)	0.0043 (8)	0.0049 (7)	0.0028 (8)
C21	0.0271 (9)	0.0372 (10)	0.0292 (9)	0.0003 (8)	0.0031 (7)	−0.0018 (8)

Geometric parameters (Å, º)

Ni1—O1	2.0421 (14)	C6—C9	1.493 (2)
Ni1—O4^i	2.0454 (13)	C7—C8	1.380 (3)
Ni1—O1W	2.0605 (16)	C7—H7	0.9300
Ni1—O2W	2.1384 (16)	C8—H8	0.9300
Ni1—N1	2.0740 (16)	N2—C19	1.324 (2)
Ni1—N2	2.0983 (16)	N2—C20	1.357 (2)
O1—C1	1.277 (2)	N1—C10	1.324 (2)
O2—C1	1.225 (2)	N1—C21	1.356 (2)
O4—C9	1.259 (2)	C10—C11	1.403 (3)
O5—C9	1.259 (2)	C10—H10	0.9300
O1W—H1W1	0.86 (2)	C11—C12	1.356 (3)
O1W—H1W2	0.85 (2)	C11—H11	0.9300
O2W—H2W1	0.85 (2)	C12—C13	1.400 (3)
O2W—H2W2	0.86 (2)	C12—H12	0.9300
O3W—H3W1	0.84 (2)	C13—C21	1.404 (3)
O3W—H3W2	0.84 (2)	C13—C14	1.430 (3)
O3—C3	1.372 (2)	C14—C15	1.350 (3)
O3—C2	1.425 (2)	C14—H14	0.9300
O4—Ni1^ii	2.0454 (13)	C15—C16	1.431 (3)
C1—C2	1.522 (3)	C15—H15	0.9300
C2—H2A	0.9700	C16—C17	1.403 (3)
C2—H2B	0.9700	C16—C20	1.407 (3)
C3—C8	1.381 (3)	C17—C18	1.359 (3)
C3—C4	1.386 (3)	C17—H17	0.9300
C4—C5	1.384 (3)	C18—C19	1.397 (3)
C4—H4	0.9300	C18—H18	0.9300
C5—C6	1.381 (3)	C19—H19	0.9300
C5—H5	0.9300	C20—C21	1.429 (3)
C6—C7	1.392 (3)
O1—Ni1—N1	175.35 (6)	C5—C6—C9	121.12 (17)
O1—Ni1—N2	95.82 (6)	C6—C5—C4	122.05 (19)
O1—Ni1—O1W	87.55 (6)	C6—C5—H5	119.0
O1—Ni1—O2W	91.48 (6)	C6—C7—H7	119.7
O1—Ni1—O4^i	93.00 (6)	C7—C6—C9	120.52 (17)
O4^i—Ni1—N1	91.64 (6)	C7—C8—C3	120.13 (19)
O4^i—Ni1—N2	171.14 (6)	C7—C8—H8	119.9
O4^i—Ni1—O1W	90.92 (6)	C8—C3—C4	120.43 (17)
O4^i—Ni1—O2W	91.28 (6)	C8—C7—C6	120.51 (19)
O1W—Ni1—N1	92.52 (6)	C8—C7—H7	119.7
O1W—Ni1—N2	90.21 (6)	C9—O4—Ni1^ii	127.27 (12)
O1W—Ni1—O2W	177.65 (6)	C10—C11—H11	120.3
O2W—Ni1—N1	88.28 (6)	C10—N1—C21	118.10 (17)
O2W—Ni1—N2	87.75 (6)	C10—N1—Ni1	128.82 (14)
N1—Ni1—N2	79.53 (6)	C11—C10—H10	118.7
Ni1—O1W—H1W1	115.1 (16)	C11—C12—C13	119.83 (19)
Ni1—O1W—H1W2	113.1 (16)	C11—C12—H12	120.1
Ni1—O2W—H2W1	93.3 (18)	C12—C11—C10	119.4 (2)
Ni1—O2W—H2W2	91.9 (17)	C12—C11—H11	120.3
O1—C1—C2	113.16 (17)	C12—C13—C14	124.0 (2)
O2—C1—C2	119.91 (18)	C12—C13—C21	117.21 (19)
O2—C1—O1	126.93 (18)	C13—C12—H12	120.1
O3—C2—C1	112.72 (16)	C13—C14—H14	119.4
O3—C2—H2A	109.0	C13—C21—C20	120.12 (17)
O3—C2—H2B	109.0	C14—C15—C16	121.08 (19)
O3—C3—C4	124.10 (18)	C14—C15—H15	119.5
O3—C3—C8	115.44 (17)	C15—C14—C13	121.28 (19)
O4—C9—C6	117.68 (17)	C15—C14—H14	119.4
O4—C9—O5	124.59 (18)	C16—C15—H15	119.5
O5—C9—C6	117.68 (17)	C16—C17—H17	120.3
N1—C10—C11	122.5 (2)	C16—C20—C21	119.73 (18)
N1—C10—H10	118.7	C17—C16—C15	123.70 (19)
N1—C21—C13	122.81 (18)	C17—C16—C20	117.33 (19)
N1—C21—C20	117.06 (16)	C17—C18—C19	119.6 (2)
N1—Ni1—N2	79.53 (6)	C17—C18—H18	120.2
N1—Ni1—O2W	88.27 (6)	C18—C17—C16	119.34 (18)
N2—C19—C18	123.03 (19)	C18—C17—H17	120.3
N2—C19—H19	118.5	C18—C19—H19	118.5
N2—C20—C16	122.94 (18)	C19—C18—H18	120.2
N2—C20—C21	117.32 (16)	C19—N2—C20	117.65 (17)
C1—C2—H2A	109.0	C19—N2—Ni1	130.17 (13)
C1—C2—H2B	109.0	C20—C16—C15	119.0 (2)
C1—O1—Ni1	126.53 (13)	C20—N2—Ni1	111.87 (12)
C3—C4—H4	120.7	C21—C13—C14	118.8 (2)
C3—C8—H8	119.9	C21—N1—Ni1	112.70 (12)
C3—O3—C2	118.82 (15)	H1W1—O1W—H1W2	108.0 (14)
C4—C5—H5	119.0	H2A—C2—H2B	107.8
C5—C4—C3	118.56 (19)	H2W1—O2W—H2W2	105.4 (13)
C5—C4—H4	120.7	H3W1—O3W—H3W2	111.3 (15)
C5—C6—C7	118.31 (17)
C3—O3—C2—C1	−70.3 (2)	C3—C4—C5—C6	−0.8 (3)
Ni1—N1—C10—C11	170.45 (15)	C4—C3—C8—C7	1.2 (3)
Ni1—N1—C21—C13	−170.38 (15)	C4—C5—C6—C7	0.9 (3)
Ni1—N1—C21—C20	10.1 (2)	C4—C5—C6—C9	−176.52 (18)
Ni1—N2—C19—C18	−171.24 (16)	C5—C6—C7—C8	0.1 (3)
Ni1—N2—C20—C16	171.32 (15)	C5—C6—C9—O4	−6.6 (3)
Ni1—N2—C20—C21	−7.8 (2)	C5—C6—C9—O5	170.67 (18)
Ni1—O1—C1—C2	172.20 (12)	C6—C7—C8—C3	−1.1 (3)
Ni1—O1—C1—O2	−7.9 (3)	C7—C6—C9—O4	175.97 (18)
Ni1^ii—O4—C9—C6	178.35 (11)	C7—C6—C9—O5	−6.7 (3)
Ni1^ii—O4—C9—O5	1.2 (3)	C8—C3—C4—C5	−0.3 (3)
O1—C1—C2—O3	173.13 (16)	C9—C6—C7—C8	177.51 (18)
O1—Ni1—N2—C19	3.44 (19)	C10—C11—C12—C13	2.7 (3)
O1—Ni1—N2—C20	−169.97 (13)	C10—N1—C21—C13	3.2 (3)
O1W—Ni1—N1—C10	86.74 (18)	C10—N1—C21—C20	−176.32 (18)
O1W—Ni1—N1—C21	−100.53 (13)	C11—C12—C13—C14	178.4 (2)
O1W—Ni1—N2—C19	−84.11 (19)	C11—C12—C13—C21	−1.5 (3)
O1W—Ni1—N2—C20	102.47 (14)	C12—C13—C14—C15	−177.6 (2)
O1W—Ni1—O1—C1	159.66 (15)	C12—C13—C21—C20	177.99 (19)
O2—C1—C2—O3	−6.7 (3)	C12—C13—C21—N1	−1.5 (3)
O2W—Ni1—N1—C10	−95.48 (18)	C13—C14—C15—C16	−0.5 (3)
O2W—Ni1—N1—C21	77.25 (13)	C14—C13—C21—C20	−1.8 (3)
O2W—Ni1—N2—C19	94.71 (19)	C14—C13—C21—N1	178.64 (18)
O2W—Ni1—N2—C20	−78.71 (14)	C14—C15—C16—C17	179.9 (2)
O2W—Ni1—O1—C1	−18.20 (15)	C14—C15—C16—C20	−1.5 (3)
O3—C3—C4—C5	−177.94 (18)	C15—C16—C17—C18	180.0 (2)
O3—C3—C8—C7	179.09 (18)	C15—C16—C20—C21	1.8 (3)
O4^i—Ni1—N1—C10	−4.25 (18)	C15—C16—C20—N2	−177.25 (18)
O4^i—Ni1—N1—C21	168.48 (13)	C16—C17—C18—C19	−2.5 (3)
O4^i—Ni1—O1—C1	−109.56 (15)	C16—C20—C21—C13	−0.2 (3)
N1—C10—C11—C12	−1.0 (3)	C16—C20—C21—N1	179.39 (18)
N1—Ni1—N2—C19	−176.6 (2)	C17—C16—C20—C21	−179.50 (18)
N1—Ni1—N2—C20	9.95 (13)	C17—C16—C20—N2	1.4 (3)
N2—C20—C21—C13	178.99 (18)	C17—C18—C19—N2	0.9 (3)
N2—C20—C21—N1	−1.5 (3)	C19—N2—C20—C16	−3.0 (3)
N2—Ni1—N1—C10	176.49 (19)	C19—N2—C20—C21	177.88 (18)
N2—Ni1—N1—C21	−10.78 (13)	C20—C16—C17—C18	1.4 (3)
N2—Ni1—O1—C1	69.69 (15)	C20—N2—C19—C18	1.9 (3)
C2—O3—C3—C4	−9.9 (3)	C21—C13—C14—C15	2.2 (3)
C2—O3—C3—C8	172.31 (18)	C21—N1—C10—C11	−1.9 (3)

Symmetry codes: (i) x, y+1, z; (ii) x, y−1, z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O2W—H2W1···O2	0.86 (2)	1.82 (2)	2.646 (2)	162 (2)
O2W—H2W2···O5^i	0.86 (2)	1.77 (2)	2.626 (2)	169 (2)
O1W—H1W1···O3W	0.86 (2)	1.84 (2)	2.706 (2)	170 (2)
O1W—H1W2···O5^iii	0.85 (2)	1.93 (2)	2.783 (2)	175 (2)
O3W—H3W2···O1^iv	0.84 (2)	2.01 (2)	2.829 (2)	163 (2)
O3W—H3W1···O3^v	0.84 (2)	1.95 (2)	2.791 (2)	172 (3)

Symmetry codes: (i) x, y+1, z; (iii) x+1, y+1, z; (iv) −x+1, −y+1, −z+1; (v) −x, −y+1, −z+1.