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In the title compound, C10H16N+·OH·3H2O, two-dimensional bilayer-like arrays of organic cations and corrugated anionic hydro­xide–water layers are stacked alternately along the c axis. All hydro­xide and water H atoms are in ordered positions, giving rise to a network of hydrogen bonds [O...O 2.639 (2)–2.927 (2) Å for water donors and O...O 3.323 (2) Å for hydro­xide donors] with four- and six-membered rings.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270100019363/de1162sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270100019363/de1162Isup2.hkl
Contains datablock I

CCDC reference: 162578

Comment top

Higher hydrates of tetraalkylammonium hydroxides crystallize as ionic clathrate hydrates (Jeffrey, 1996), and the crystal structures of the ten existing hydrates of tetramethylammonium hydroxide with at least four water molecules per base molecule have been determined by single-crystal X-ray diffraction methods which did not reveal conclusively the H-atom positions in cases of disorder (McMullan et al., 1966; Mootz & Seidel, 1990; Mootz & Stäben, 1992; Hesse & Jansen, 1991). The hydrogen-bonding systems of those three-dimensional anionic host structures have therefore been interpreted by evaluating the oxygen-oxygen distances and assuming that every H atom is involved in hydrogen-bonding interactions. However, our recent X-ray structural study on tetraethylammonium nonahydrate, a novel ionic clathrate hydrate, gave some indications that the latter assumption need not be valid (Wiebcke & Felsche, 2000a). Also, detailed structural information about lower non-clathrate hydrates of alkylammonium hydroxides is scarce. The crystal structures of the dihydrates of tetramethylammonium (Mootz & Seidel, 1990) and N,N-dimethylpyrrolidinium hydroxide (Stäben et al., 1998), as well as of the tetra- and pentahydrate of tetraethylammonium hydroxide (Wiebcke & Felsche, 2000b,c) are available. Here we report a single-crystal X-ray structure analysis of benzyltrimethylammonium hydroxide trihydrate, (I), which possesses a novel layered structure. \sch

The molecular details and atomic numbering are displayed in Fig. 1. As can be seen in Fig. 2a, the NBnNMe3+ cations of nearly ideal m (Cs) molecular symmetry are assembled into two-dimensional, bilayer-like arrays parallel to (001) which are interleaved by corrugated anionic hydroxide-water layers. Each anionic layer (Fig. 2 b) is based on a planar (3,5)-connected net with a ratio of three- to five-connected nodes of 3:1 [the short Schläfli symbol (O'Keeffe & Brese, 1992) is (42.6),(4.62)2,(43.62)]. This net contains four- and six-membered rings in the ratio 2:1.

The five-connected nodes are occupied by the hydroxide ions (atom O1) which posses a distorted square-pyramidal coordination by water molecules (Fig. 1). The ions are acceptors and donors in the hydrogen bonds with the equatorial and apical water molecules, respectively. Each water molecule (atoms O2, O3, O4) donates two and accepts one hydrogen bond. The well known differences in donor and acceptor strength of the OH- and H2O species is clearly reflected in the hydrogen-bonding geometries which are listed in Table 1. In particular, the OH-···OH2 interactions [O1···O3i 3.323 (2) Å, i: x, y + 1, z] are by far the longest (weakest) hydrogen bonds. As can be seen in Figs. 2a and 2 b, flat ribbons containing exclusively shorter hydrogen bonds donated by the water molecules [O···O 2.639 (2)–2.927 (2) Å] and running along the [100] direction can be identified. These ribbons are linked by long OH-···OH2 bonds into the corrugated anionic layers. The crystallographically distinct four- and six-membered oxygen rings are also shown in Fig. 1.

Within the organic bilayers, all aryl rings are oriented approximately perpendicular to the [010] direction, and pairs of cations (across inversion centres at 1/2,0,0) have interring distances (3.40 Å) and ring-centroid offsets (1.38 Å) that are indicative of attractive face-to-face (ff) aryl-aryl interactions (Hunter, 1994). Futher close ff contacts are hindered by the NMe3 moieties which protrude to one side of an aryl ring. Of the numerous C–H···O interactions which may be very weak hydrogen bonds (Steiner & Desiraju, 1998), only the shortest are listed in Table 1. It should be noted that the C–H···O contact at the OH - ion in trans position to the hydroxide proton is rather long [H8···O1 2.96 (3), C8···O1 3.817 (3) Å, C8–H8···O1 158 (2) °]. Possibly, this is because the O atom is well coordinated by O—H···O hydrogen bonds.

Coordination and bonding observed for the OH- ion in NBnMe3OH·3H2O, i.e., donor in one and acceptor in four O–H···O bonds, is as yet uncommon in crystalline alkylammonium and metal hydroxide hydrates. Similar geometries exist only in CsOH. 2H2O and CsOH·3H2O, if weak interactions with the caesium cations are not taken into account (Mootz & Rütter, 1992).

Related literature top

For related literature, see: Hesse & Jansen (1991); Hunter (1994); Jeffrey (1996); McMullan et al. (1966); Mootz & Rütter (1992); Mootz & Seidel (1990); Mootz & Stäben (1992); O'Keeffe & Brese (1992); Stäben (1998); Steiner & Desiraju (1998); Wiebcke & Felsche (2000a, 2000b, 2000c).

Experimental top

Removal of water in vacuo from an aqueous solution of NBnMe3OH (Fluka, ca 40%) at room temperature yielded air-sentitive crystals of NBnMe3OH·3H2O. A suitable crystal was embebbed in a droplet of perfuorinated polyether oil for protaction and freeze-fixed on the tip of a glass fibre at the low temperature of the X-ray measurements.

Refinement top

All H atoms were located on a difference Fourier map and refined independently [C–H 0.91 (2)–1.01 (3) Å].

Computing details top

Data collection: CAD-4 Software (Enraf-Nonius, 1994); cell refinement: CAD-4 Software; data reduction: XCAD4 (Harms & Wocadlo, 1995) and WinGX (Farrugia, 1999); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg & Berndt, 1999); software used to prepare material for publication: SHELXL97.

Figures top
[Figure 1] Fig. 1. The molecular view (DIAMOND; Brandenburg & Berndt, 1999) of (I) showing the local surrounding of the hydroxide ion, including the distinct four- and six-membered oxygen rings and one organic cation. Displacement ellipsoids are drawn at the 70% probability level and H atoms are shown as small spheres of arbitrary radii. [Symmetry code: (i) -x + 1, -y + 1,-z + 1; (ii) x + 1, y, z; (iii) -x, -y + 1, -z + 1; (iv) x - 1, y, z; (v) -x, -y + 2, -z + 1; (vi) x, y + 1, z; (vii) -x + 1, -y + 2, -z + 1].
[Figure 2] Fig. 2. (a) The layered structure as seen along the a axis; only non-H atoms are shown. (b) One hydroxide-water layer as seen along the c axis, with N atoms of adjacent NBnMe3+ cations; + and - symbols distinguish between N atoms lying directly above and below the given layer. Large open spheres are N and C atoms of cations, medium-sized black spheres are water O atoms, medium-sized open spheres are hydroxide O atoms and small open spheres are H atoms. Dashed lines indicate the long OH-···OH2 hydrogen bonds (DIAMOND; Brandenburg & Berndt, 1999).
(I) top
Crystal data top
C10H23NO4Z = 2
Mr = 221.29F(000) = 244
Triclinic, P1Dx = 1.212 Mg m3
a = 6.337 (1) ÅMo Kα radiation, λ = 0.71073 Å
b = 8.028 (1) ÅCell parameters from 25 reflections
c = 12.169 (2) Åθ = 10.7–24.2°
α = 80.53 (1)°µ = 0.09 mm1
β = 84.12 (1)°T = 183 K
γ = 85.40 (1)°Needle, white
V = 606.2 (2) Å30.55 × 0.25 × 0.23 mm
Data collection top
Enraf-Nonius
diffractometer
θmax = 26.9°, θmin = 2.6°
ω/2θ scansh = 08
2854 measured reflectionsk = 1010
2610 independent reflectionsl = 1515
1922 reflections with I > 2σ(I)3 standard reflections every 200 reflections
Rint = 0.051 intensity decay: negligigle
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullHydrogen site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.055All H-atom parameters refined
wR(F2) = 0.161 w = 1/[σ2(Fo2) + (0.1127P)2 + 0.0601P]
where P = (Fo2 + 2Fc2)/3
S = 1.01(Δ/σ)max < 0.001
2610 reflectionsΔρmax = 0.42 e Å3
228 parametersΔρmin = 0.29 e Å3
0 restraints
Crystal data top
C10H23NO4γ = 85.40 (1)°
Mr = 221.29V = 606.2 (2) Å3
Triclinic, P1Z = 2
a = 6.337 (1) ÅMo Kα radiation
b = 8.028 (1) ŵ = 0.09 mm1
c = 12.169 (2) ÅT = 183 K
α = 80.53 (1)°0.55 × 0.25 × 0.23 mm
β = 84.12 (1)°
Data collection top
Enraf-Nonius
diffractometer
Rint = 0.051
2854 measured reflections3 standard reflections every 200 reflections
2610 independent reflections intensity decay: negligigle
1922 reflections with I > 2σ(I)
Refinement top
R[F2 > 2σ(F2)] = 0.0550 restraints
wR(F2) = 0.161All H-atom parameters refined
S = 1.01Δρmax = 0.42 e Å3
2610 reflectionsΔρmin = 0.29 e Å3
228 parameters
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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O10.3916 (2)0.76720 (18)0.45063 (14)0.0277 (4)
O20.0615 (2)0.75834 (19)0.33643 (13)0.0275 (3)
O30.3194 (3)0.01205 (18)0.64828 (13)0.0298 (4)
O40.7377 (2)0.5463 (2)0.43543 (14)0.0304 (4)
H10.369 (5)0.809 (4)0.506 (2)0.040 (8)*
H310.418 (5)0.086 (4)0.621 (2)0.051 (8)*
H420.630 (5)0.617 (4)0.450 (2)0.057 (9)*
H320.200 (5)0.079 (4)0.661 (2)0.054 (8)*
H210.170 (6)0.757 (5)0.379 (3)0.081 (11)*
H220.017 (5)0.693 (4)0.378 (3)0.053 (8)*
H410.697 (5)0.450 (5)0.474 (2)0.052 (8)*
N0.8182 (2)0.74174 (19)0.27345 (12)0.0199 (4)
C10.8718 (3)0.8174 (3)0.39317 (17)0.0281 (5)
H1A0.997 (5)0.888 (4)0.395 (2)0.051 (8)*
H1B0.744 (4)0.888 (3)0.4205 (19)0.031 (6)*
H1C0.908 (3)0.725 (3)0.4389 (18)0.024 (6)*
C21.0127 (4)0.6449 (3)0.2302 (2)0.0353 (5)
H2A1.131 (5)0.724 (4)0.235 (2)0.047 (8)*
H2B1.061 (4)0.563 (3)0.281 (2)0.032 (6)*
H2C0.975 (4)0.590 (3)0.155 (2)0.040 (7)*
C30.6438 (4)0.6258 (3)0.2697 (2)0.0325 (5)
H3A0.609 (4)0.580 (3)0.188 (2)0.031 (6)*
H3B0.702 (5)0.532 (4)0.312 (2)0.052 (8)*
H3C0.520 (6)0.692 (4)0.304 (3)0.065 (10)*
C40.7471 (3)0.8857 (2)0.20742 (16)0.0218 (4)
H4A0.863 (4)0.959 (3)0.2199 (17)0.021 (5)*
H4B0.624 (4)0.942 (3)0.2402 (19)0.026 (6)*
C50.6944 (3)0.8292 (2)0.08423 (15)0.0193 (4)
C60.4865 (3)0.7959 (2)0.04180 (17)0.0244 (4)
H60.379 (4)0.810 (3)0.100 (2)0.039 (7)*
C70.4352 (3)0.7539 (3)0.07181 (17)0.0271 (4)
H70.291 (4)0.729 (3)0.104 (2)0.038 (7)*
C80.5892 (3)0.7457 (2)0.14591 (17)0.0260 (4)
H80.564 (4)0.722 (3)0.221 (2)0.025 (6)*
C90.7964 (3)0.7798 (2)0.10528 (17)0.0259 (4)
H90.897 (4)0.781 (3)0.159 (2)0.037 (7)*
C100.8481 (3)0.8216 (2)0.00878 (16)0.0224 (4)
H100.991 (3)0.849 (3)0.0362 (17)0.017 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0186 (7)0.0235 (7)0.0408 (9)0.0017 (5)0.0047 (6)0.0051 (6)
O20.0222 (7)0.0281 (7)0.0311 (8)0.0047 (6)0.0038 (6)0.0006 (6)
O30.0260 (8)0.0211 (7)0.0414 (9)0.0011 (6)0.0058 (6)0.0011 (6)
O40.0185 (7)0.0224 (7)0.0481 (9)0.0009 (6)0.0064 (6)0.0051 (7)
N0.0170 (7)0.0176 (7)0.0253 (8)0.0016 (6)0.0023 (6)0.0051 (6)
C10.0289 (10)0.0314 (11)0.0245 (10)0.0050 (9)0.0000 (8)0.0057 (8)
C20.0312 (12)0.0394 (13)0.0362 (12)0.0196 (10)0.0110 (9)0.0140 (10)
C30.0323 (11)0.0292 (11)0.0385 (12)0.0133 (9)0.0040 (9)0.0113 (9)
C40.0237 (9)0.0154 (8)0.0262 (9)0.0029 (7)0.0033 (7)0.0041 (7)
C50.0185 (8)0.0128 (7)0.0263 (9)0.0031 (6)0.0023 (7)0.0043 (7)
C60.0173 (9)0.0243 (9)0.0322 (10)0.0034 (7)0.0029 (7)0.0080 (8)
C70.0221 (10)0.0257 (10)0.0331 (11)0.0024 (8)0.0028 (8)0.0060 (8)
C80.0339 (11)0.0205 (9)0.0220 (10)0.0001 (8)0.0009 (8)0.0016 (7)
C90.0268 (10)0.0231 (9)0.0289 (10)0.0030 (8)0.0088 (8)0.0060 (7)
C100.0156 (8)0.0216 (9)0.0307 (10)0.0002 (7)0.0033 (7)0.0064 (7)
Geometric parameters (Å, º) top
O1—O22.639 (2)C1—H1A1.00 (3)
O1—O3i2.704 (2)C1—H1B1.00 (3)
O1—O42.719 (2)C1—H1C1.00 (2)
O1—O4i2.806 (2)C2—H2A1.01 (3)
O1—O3ii3.323 (2)C2—H2B0.98 (3)
O1—H10.80 (3)C2—H2C0.96 (3)
O2—O4iii2.818 (2)C3—H3A1.01 (2)
O2—O3iv2.927 (2)C3—H3B1.01 (3)
O2—H210.90 (4)C3—H3C1.00 (4)
O2—H220.83 (4)C4—C51.504 (3)
O3—O1i2.704 (2)C4—H4A0.97 (2)
O3—O2iv2.927 (2)C4—H4B0.96 (2)
O3—O1v3.323 (2)C5—C61.395 (3)
O3—H310.90 (3)C5—C101.397 (3)
O3—H320.91 (3)C6—C71.379 (3)
O4—O1i2.806 (2)C6—H61.01 (3)
O4—O2vi2.818 (2)C7—C81.386 (3)
O4—O4i3.332 (3)C7—H70.98 (3)
O4—H420.87 (4)C8—C91.387 (3)
O4—H410.88 (4)C8—H80.91 (2)
N—C31.494 (2)C9—C101.385 (3)
N—C21.498 (2)C9—H90.95 (3)
N—C11.499 (2)C10—H100.96 (2)
N—C41.527 (2)
O2—O1—O3i114.74 (7)H42—O4—H41103 (3)
O2—O1—O4121.84 (8)C3—N—C2110.33 (17)
O3i—O1—O481.07 (6)C3—N—C1108.02 (15)
O2—O1—O4i84.03 (6)C2—N—C1108.38 (16)
O3i—O1—O4i154.53 (7)C3—N—C4110.99 (15)
O4—O1—O4i74.16 (6)C2—N—C4110.87 (15)
O2—O1—O3ii115.54 (6)C1—N—C4108.15 (14)
O3i—O1—O3ii84.93 (6)N—C1—H1A107.1 (16)
O4—O1—O3ii121.61 (7)N—C1—H1B108.2 (13)
O4i—O1—O3ii102.94 (6)H1A—C1—H1B112 (2)
O2—O1—H1116 (2)N—C1—H1C109.3 (12)
O3i—O1—H195 (2)H1A—C1—H1C111 (2)
O4—O1—H1117 (2)H1B—C1—H1C109.6 (18)
O4i—O1—H192 (2)N—C2—H2A110.0 (17)
O3ii—O1—H112 (2)N—C2—H2B107.5 (14)
O1—O2—O4iii117.60 (7)H2A—C2—H2B106 (2)
O1—O2—O3iv123.33 (7)N—C2—H2C108.1 (17)
O4iii—O2—O3iv75.67 (6)H2A—C2—H2C113 (2)
O1—O2—H214 (2)H2B—C2—H2C112 (2)
O4iii—O2—H21114 (2)N—C3—H3A105.9 (13)
O3iv—O2—H21123 (2)N—C3—H3B107.1 (17)
O1—O2—H22104 (2)H3A—C3—H3B111 (2)
O4iii—O2—H2213 (2)N—C3—H3C108.4 (19)
O3iv—O2—H2282 (2)H3A—C3—H3C112 (2)
H21—O2—H22101 (3)H3B—C3—H3C112 (2)
O1i—O3—O2iv100.40 (6)C5—C4—N114.26 (14)
O1i—O3—O1v95.07 (6)C5—C4—H4A110.5 (12)
O2iv—O3—O1v120.34 (6)N—C4—H4A105.4 (13)
O1i—O3—H314.6 (18)C5—C4—H4B109.8 (13)
O2iv—O3—H31100.7 (19)N—C4—H4B105.8 (14)
O1v—O3—H3198.7 (18)H4A—C4—H4B111 (2)
O1i—O3—H32104.0 (19)C6—C5—C10118.37 (17)
O2iv—O3—H326.0 (19)C6—C5—C4120.54 (17)
O1v—O3—H32124.1 (19)C10—C5—C4120.91 (17)
H31—O3—H32104 (3)C7—C6—C5120.67 (18)
O1—O4—O1i105.84 (6)C7—C6—H6124.1 (15)
O1—O4—O2vi102.83 (7)C5—C6—H6115.2 (14)
O1i—O4—O2vi150.49 (7)C6—C7—C8120.50 (18)
O1—O4—O4i54.12 (5)C6—C7—H7122.3 (14)
O1i—O4—O4i51.72 (5)C8—C7—H7117.2 (14)
O2vi—O4—O4i156.10 (9)C9—C8—C7119.62 (18)
O1—O4—H427.7 (19)C9—C8—H8116.0 (15)
O1i—O4—H42104 (2)C7—C8—H8124.3 (15)
O2vi—O4—H42104 (2)C10—C9—C8119.92 (18)
O4i—O4—H4253 (2)C10—C9—H9122.3 (15)
O1—O4—H41105 (2)C8—C9—H9117.6 (15)
O1i—O4—H412.5 (19)C9—C10—C5120.92 (17)
O2vi—O4—H41151 (2)C9—C10—H10119.4 (12)
O4i—O4—H4151 (2)C5—C10—H10119.7 (12)
Symmetry codes: (i) x+1, y+1, z+1; (ii) x, y+1, z; (iii) x1, y, z; (iv) x, y+1, z+1; (v) x, y1, z; (vi) x+1, y, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O3ii0.80 (3)2.55 (3)3.323 (2)165 (3)
O2—H21···O10.90 (4)1.74 (4)2.639 (2)174 (4)
O2—H22···O4iii0.83 (4)2.02 (4)2.818 (2)161 (3)
O3—H31···O1i0.90 (3)1.81 (3)2.704 (2)173 (3)
O3—H32···O2iv0.91 (3)2.03 (4)2.927 (2)171 (3)
O4—H42···O10.87 (4)1.86 (4)2.719 (2)169 (3)
O4—H41···O1i0.88 (4)1.93 (4)2.806 (2)176 (3)
C1—H1A···O3vii1.01 (3)2.49 (3)3.465 (3)165 (2)
C2—H2B···O4viii0.99 (2)2.41 (2)3.340 (3)158 (2)
C4—H4A···O2ix0.96 (3)2.52 (2)3.285 (2)136 (2)
C4—H4B···O3x0.96 (2)2.45 (2)3.377 (3)163 (2)
C9—H9···O2vi0.96 (2)2.47 (2)3.395 (3)163 (2)
Symmetry codes: (i) x+1, y+1, z+1; (ii) x, y+1, z; (iii) x1, y, z; (iv) x, y+1, z+1; (vi) x+1, y, z; (vii) x+1, y+1, z1; (viii) x+2, y+1, z; (ix) x+1, y+2, z; (x) x, y+1, z1.

Experimental details

Crystal data
Chemical formulaC10H23NO4
Mr221.29
Crystal system, space groupTriclinic, P1
Temperature (K)183
a, b, c (Å)6.337 (1), 8.028 (1), 12.169 (2)
α, β, γ (°)80.53 (1), 84.12 (1), 85.40 (1)
V3)606.2 (2)
Z2
Radiation typeMo Kα
µ (mm1)0.09
Crystal size (mm)0.55 × 0.25 × 0.23
Data collection
DiffractometerEnraf-Nonius
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
2854, 2610, 1922
Rint0.051
(sin θ/λ)max1)0.637
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.055, 0.161, 1.01
No. of reflections2610
No. of parameters228
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)0.42, 0.29

Computer programs: CAD-4 Software (Enraf-Nonius, 1994), CAD-4 Software, XCAD4 (Harms & Wocadlo, 1995) and WinGX (Farrugia, 1999), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), DIAMOND (Brandenburg & Berndt, 1999), SHELXL97.

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O3i0.80 (3)2.55 (3)3.323 (2)165 (3)
O2—H21···O10.90 (4)1.74 (4)2.639 (2)174 (4)
O2—H22···O4ii0.83 (4)2.02 (4)2.818 (2)161 (3)
O3—H31···O1iii0.90 (3)1.81 (3)2.704 (2)173 (3)
O3—H32···O2iv0.91 (3)2.03 (4)2.927 (2)171 (3)
O4—H42···O10.87 (4)1.86 (4)2.719 (2)169 (3)
O4—H41···O1iii0.88 (4)1.93 (4)2.806 (2)176 (3)
C1—H1A···O3v1.01 (3)2.49 (3)3.465 (3)165 (2)
C2—H2B···O4vi0.99 (2)2.41 (2)3.340 (3)158 (2)
C4—H4A···O2vii0.96 (3)2.52 (2)3.285 (2)136 (2)
C4—H4B···O3viii0.96 (2)2.45 (2)3.377 (3)163 (2)
C9—H9···O2ix0.96 (2)2.47 (2)3.395 (3)163 (2)
Symmetry codes: (i) x, y+1, z; (ii) x1, y, z; (iii) x+1, y+1, z+1; (iv) x, y+1, z+1; (v) x+1, y+1, z1; (vi) x+2, y+1, z; (vii) x+1, y+2, z; (viii) x, y+1, z1; (ix) x+1, y, z.
 

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