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The binary phosphide penta­nickel tetra­phosphide, Ni5P4, has been reinvestigated, leading to improved reliability factors than found previously [Elfström (1965), Acta Chem. Scand. 19, 1694-1704] and inclusion of anisotropic displacement parameters.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807028164/mg2021sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536807028164/mg2021Isup2.hkl
Contains datablock I

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](P-P) = 0.001 Å
  • R factor = 0.027
  • wR factor = 0.034
  • Data-to-parameter ratio = 25.7

checkCIF/PLATON results

No syntax errors found



Alert level B PLAT031_ALERT_4_B Refined Extinction Parameter within Range ...... 2.38 Sigma
Alert level C STRVA01_ALERT_4_C Flack test results are ambiguous. From the CIF: _refine_ls_abs_structure_Flack 0.557 From the CIF: _refine_ls_abs_structure_Flack_su 0.016 PLAT731_ALERT_1_C Bond Calc 2.6350(4), Rep 2.6349(9) ...... 2.25 su-Ra NI1 -NI1 1.555 3.655 PLAT731_ALERT_1_C Bond Calc 2.5743(4), Rep 2.5744(9) ...... 2.25 su-Ra NI3 -NI3 1.555 3.655
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 40.02 From the CIF: _reflns_number_total 1079 Count of symmetry unique reflns 561 Completeness (_total/calc) 192.34% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 518 Fraction of Friedel pairs measured 0.923 Are heavy atom types Z>Si present yes PLAT033_ALERT_2_G Flack Parameter Value Deviates 2 * su from zero. 0.56 PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature 293 K PLAT200_ALERT_1_G Check the Reported _diffrn_ambient_temperature . 293 K PLAT792_ALERT_1_G Check the Absolute Configuration of P3 = ... S PLAT860_ALERT_3_G Note: Number of Least-Squares Restraints ....... 1
0 ALERT level A = In general: serious problem 1 ALERT level B = Potentially serious problem 3 ALERT level C = Check and explain 6 ALERT level G = General alerts; check 5 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 1 ALERT type 2 Indicator that the structure model may be wrong or deficient 1 ALERT type 3 Indicator that the structure quality may be low 3 ALERT type 4 Improvement, methodology, query or suggestion 0 ALERT type 5 Informative message, check
checkCIF publication errors
Alert level A PUBL024_ALERT_1_A The number of authors is greater than 5. Please specify the role of each of the co-authors for your paper.
Author Response: I shall specify the role of each of co-authors: Zelinska M. -- the experimental work: synthes and previous investigation of the single crystal; the writing of the publication. Oryshchyn S.V. -- calculation which were concerned with the refinement of the crystal structure of Ni5P4.Zhak O.V. - co-author of the writing this publication;Pivan J-Y. - interpretation and conclusion of the obtained results. Potel M. - the obtaining of the experimental data of NI5P4 by the single crystal method (laboratory of the university Rennes1). Noel H.- confirming the results of the single-crystal diffraction by the EDS-analysis.


1 ALERT level A = Data missing that is essential or data in wrong format 0 ALERT level G = General alerts. Data that may be required is missing

Computing details top

Data collection: COLLECT (Nonius, 1998); cell refinement: DIRAX/LS (Duisenberg et al., 2003); data reduction: EVALCCD (Duisenberg et al., 2003); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: WinGX (Farrugia, 1999).

pentanickel tetraphosphide top
Crystal data top
Ni5P4Dx = 6.313 Mg m3
Mr = 417.33Mo Kα radiation, λ = 0.71069 Å
Hexagonal, P63mcCell parameters from 13186 reflections
Hall symbol: P 6c -2cθ = 2.0–42.1°
a = 6.7921 (1) ŵ = 22.31 mm1
c = 10.9922 (2) ÅT = 293 K
V = 439.16 (1) Å3Prism, black
Z = 40.05 × 0.03 × 0.02 mm
F(000) = 800
Data collection top
Nonius KappaCCD
diffractometer
1079 independent reflections
Radiation source: fine-focus sealed tube896 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.082
Detector resolution: 9 pixels mm-1θmax = 40.0°, θmin = 3.5°
CCD rotation images, thick slices scansh = 1212
Absorption correction: multi-scan
(Blessing, 1995)
k = 1112
Tmin = 0.472, Tmax = 0.745l = 1919
19002 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: full w = 1/[σ2(Fo2) + (0.0109P)2 + 0.4236P]
where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.027(Δ/σ)max < 0.001
wR(F2) = 0.034Δρmax = 1.15 e Å3
S = 1.06Δρmin = 1.06 e Å3
1079 reflectionsExtinction correction: SHELXL97 (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
42 parametersExtinction coefficient: 0.00038 (16)
1 restraintAbsolute structure: Flack (1983), with how many Friedel pairs?
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.557 (16)
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
Ni10.53735 (4)0.46265 (4)0.08904 (3)0.00558 (12)
Ni20.20756 (3)0.79244 (3)0.23708 (6)0.00558 (7)
Ni30.54033 (4)0.45967 (4)0.37948 (3)0.00535 (12)
Ni40.00000.00000.20081 (7)0.00561 (15)
P10.81828 (6)0.18172 (6)0.23166 (12)0.00460 (13)
P20.17832 (8)0.82168 (8)0.44259 (9)0.00494 (16)
P30.00000.00000.00000 (17)0.0054 (3)
P40.33330.66670.05931 (14)0.0059 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ni10.00558 (18)0.00558 (18)0.0047 (3)0.00216 (18)0.00007 (10)0.00007 (10)
Ni20.00532 (12)0.00532 (12)0.00664 (15)0.00306 (14)0.00029 (12)0.00029 (12)
Ni30.00510 (19)0.00510 (19)0.0060 (3)0.00268 (19)0.00042 (9)0.00042 (9)
Ni40.0041 (2)0.0041 (2)0.0086 (3)0.00206 (10)0.0000.000
P10.0044 (2)0.0044 (2)0.0049 (3)0.0021 (3)0.0005 (2)0.0005 (2)
P20.0044 (3)0.0044 (3)0.0056 (3)0.0019 (3)0.00014 (15)0.00014 (15)
P30.0047 (4)0.0047 (4)0.0069 (9)0.00237 (19)0.0000.000
P40.0059 (4)0.0059 (4)0.0059 (6)0.00293 (19)0.0000.000
Geometric parameters (Å, º) top
Ni1—P1i2.2891 (10)Ni3—Ni2vi2.6394 (6)
Ni1—P1ii2.2891 (10)Ni4—P1ii2.1645 (7)
Ni1—P2iii2.3361 (8)Ni4—P1xii2.1645 (7)
Ni1—P2iv2.3361 (8)Ni4—P1xiii2.1645 (7)
Ni1—P42.4223 (5)Ni4—P32.207 (2)
Ni1—Ni3v2.4782 (5)Ni4—Ni2vii2.4742 (4)
Ni1—Ni1ii2.6349 (9)Ni4—Ni2xiv2.4742 (4)
Ni1—Ni1i2.6349 (9)Ni4—Ni2xv2.4742 (4)
Ni1—Ni2vi2.6545 (6)P1—Ni4xvi2.1645 (7)
Ni1—Ni2vii2.6545 (6)P1—Ni1i2.2891 (10)
Ni2—P22.2850 (11)P1—Ni1ii2.2891 (10)
Ni2—P1viii2.3057 (4)P1—Ni2xvii2.3057 (4)
Ni2—P1ix2.3057 (4)P1—Ni2xviii2.3057 (4)
Ni2—P42.4510 (14)P1—Ni3ii2.3194 (10)
Ni2—Ni4x2.4742 (4)P1—Ni3i2.3194 (10)
Ni2—Ni2vi2.5627 (6)P2—P3xix2.1907 (10)
Ni2—Ni2vii2.5627 (6)P2—Ni3vi2.3012 (5)
Ni2—Ni3vii2.6394 (6)P2—Ni3vii2.3012 (5)
Ni2—Ni3vi2.6394 (6)P2—Ni1xx2.3361 (8)
Ni2—Ni1vi2.6545 (6)P2—Ni1xxi2.3361 (8)
Ni2—Ni1vii2.6545 (6)P3—P2xxii2.1907 (10)
Ni3—P2vi2.3012 (5)P3—P2iii2.1907 (10)
Ni3—P2vii2.3012 (5)P3—P2xxiii2.1907 (10)
Ni3—P1ii2.3194 (10)P4—Ni1vii2.4223 (5)
Ni3—P1i2.3194 (10)P4—Ni1vi2.4223 (5)
Ni3—P4xi2.4731 (13)P4—Ni2vi2.4510 (14)
Ni3—Ni1xi2.4782 (5)P4—Ni2vii2.4510 (14)
Ni3—Ni3ii2.5744 (9)P4—Ni3xxiv2.4731 (13)
Ni3—Ni3i2.5744 (9)P4—Ni3xxv2.4731 (13)
Ni3—Ni2vii2.6394 (6)P4—Ni3v2.4731 (13)
P1i—Ni1—P1ii84.88 (5)P2vii—Ni3—Ni3i103.30 (2)
P1i—Ni1—P2iii148.92 (3)P1ii—Ni3—Ni3i56.292 (19)
P1ii—Ni1—P2iii86.79 (3)P1i—Ni3—Ni3i96.374 (19)
P1i—Ni1—P2iv86.79 (3)P4xi—Ni3—Ni3i58.636 (19)
P1ii—Ni1—P2iv148.92 (3)Ni1xi—Ni3—Ni3i108.624 (10)
P2iii—Ni1—P2iv85.07 (5)Ni3ii—Ni3—Ni3i60.0
P1i—Ni1—P4111.40 (3)P2vi—Ni3—Ni2vii94.98 (3)
P1ii—Ni1—P4111.40 (3)P2vii—Ni3—Ni2vii54.58 (3)
P2iii—Ni1—P499.53 (3)P1ii—Ni3—Ni2vii54.958 (18)
P2iv—Ni1—P499.53 (3)P1i—Ni3—Ni2vii94.16 (3)
P1i—Ni1—Ni3v137.56 (3)P4xi—Ni3—Ni2vii149.322 (14)
P1ii—Ni1—Ni3v137.56 (3)Ni1xi—Ni3—Ni2vii108.33 (2)
P2iii—Ni1—Ni3v57.019 (19)Ni3ii—Ni3—Ni2vii143.035 (15)
P2iv—Ni1—Ni3v57.019 (19)Ni3i—Ni3—Ni2vii108.272 (11)
P4—Ni1—Ni3v60.61 (4)P2vi—Ni3—Ni2vi54.58 (3)
P1i—Ni1—Ni1ii54.86 (2)P2vii—Ni3—Ni2vi94.98 (3)
P1ii—Ni1—Ni1ii95.697 (19)P1ii—Ni3—Ni2vi94.16 (3)
P2iii—Ni1—Ni1ii96.43 (2)P1i—Ni3—Ni2vi54.958 (18)
P2iv—Ni1—Ni1ii55.670 (17)P4xi—Ni3—Ni2vi149.322 (14)
P4—Ni1—Ni1ii149.104 (9)Ni1xi—Ni3—Ni2vi108.33 (2)
Ni3v—Ni1—Ni1ii108.624 (10)Ni3ii—Ni3—Ni2vi108.272 (11)
P1i—Ni1—Ni1i95.697 (19)Ni3i—Ni3—Ni2vi143.035 (15)
P1ii—Ni1—Ni1i54.86 (2)Ni2vii—Ni3—Ni2vi58.09 (2)
P2iii—Ni1—Ni1i55.670 (17)P1ii—Ni4—P1xii117.592 (19)
P2iv—Ni1—Ni1i96.43 (2)P1ii—Ni4—P1xiii117.592 (19)
P4—Ni1—Ni1i149.104 (9)P1xii—Ni4—P1xiii117.592 (19)
Ni3v—Ni1—Ni1i108.623 (10)P1ii—Ni4—P399.01 (4)
Ni1ii—Ni1—Ni1i60.0P1xii—Ni4—P399.01 (4)
P1i—Ni1—Ni2vi55.001 (18)P1xiii—Ni4—P399.01 (4)
P1ii—Ni1—Ni2vi94.47 (3)P1ii—Ni4—Ni2vii59.162 (4)
P2iii—Ni1—Ni2vi155.78 (3)P1xii—Ni4—Ni2vii161.71 (5)
P2iv—Ni1—Ni2vi105.03 (2)P1xiii—Ni4—Ni2vii59.162 (4)
P4—Ni1—Ni2vi57.52 (3)P3—Ni4—Ni2vii99.27 (2)
Ni3v—Ni1—Ni2vi109.83 (2)P1ii—Ni4—Ni2xiv161.71 (5)
Ni1ii—Ni1—Ni2vi107.477 (12)P1xii—Ni4—Ni2xiv59.162 (4)
Ni1i—Ni1—Ni2vi141.539 (16)P1xiii—Ni4—Ni2xiv59.162 (4)
P1i—Ni1—Ni2vii94.47 (3)P3—Ni4—Ni2xiv99.27 (2)
P1ii—Ni1—Ni2vii55.001 (18)Ni2vii—Ni4—Ni2xiv117.456 (12)
P2iii—Ni1—Ni2vii105.03 (2)P1ii—Ni4—Ni2xv59.162 (4)
P2iv—Ni1—Ni2vii155.78 (3)P1xii—Ni4—Ni2xv59.162 (4)
P4—Ni1—Ni2vii57.52 (3)P1xiii—Ni4—Ni2xv161.71 (5)
Ni3v—Ni1—Ni2vii109.83 (2)P3—Ni4—Ni2xv99.27 (2)
Ni1ii—Ni1—Ni2vii141.539 (16)Ni2vii—Ni4—Ni2xv117.456 (12)
Ni1i—Ni1—Ni2vii107.477 (12)Ni2xiv—Ni4—Ni2xv117.456 (12)
Ni2vi—Ni1—Ni2vii57.72 (2)Ni4xvi—P1—Ni1i109.52 (4)
P2—Ni2—P1viii86.32 (4)Ni4xvi—P1—Ni1ii109.52 (4)
P2—Ni2—P1ix86.32 (4)Ni1i—P1—Ni1ii70.27 (4)
P1viii—Ni2—P1ix106.83 (4)Ni4xvi—P1—Ni2xvii67.127 (19)
P2—Ni2—P4151.53 (4)Ni1i—P1—Ni2xvii136.32 (5)
P1viii—Ni2—P4109.81 (4)Ni1ii—P1—Ni2xvii70.58 (2)
P1ix—Ni2—P4109.81 (4)Ni4xvi—P1—Ni2xviii67.127 (19)
P2—Ni2—Ni4x90.61 (3)Ni1i—P1—Ni2xviii70.58 (2)
P1viii—Ni2—Ni4x53.711 (19)Ni1ii—P1—Ni2xviii136.32 (5)
P1ix—Ni2—Ni4x53.712 (19)Ni2xvii—P1—Ni2xviii133.03 (4)
P4—Ni2—Ni4x117.86 (4)Ni4xvi—P1—Ni3ii123.56 (4)
P2—Ni2—Ni2vi97.49 (2)Ni1i—P1—Ni3ii126.78 (3)
P1viii—Ni2—Ni2vi156.517 (19)Ni1ii—P1—Ni3ii87.701 (18)
P1ix—Ni2—Ni2vi96.558 (19)Ni2xvii—P1—Ni3ii69.59 (2)
P4—Ni2—Ni2vi58.48 (2)Ni2xviii—P1—Ni3ii132.01 (5)
Ni4x—Ni2—Ni2vi148.728 (6)Ni4xvi—P1—Ni3i123.56 (4)
P2—Ni2—Ni2vii97.49 (2)Ni1i—P1—Ni3i87.701 (18)
P1viii—Ni2—Ni2vii96.558 (19)Ni1ii—P1—Ni3i126.78 (3)
P1ix—Ni2—Ni2vii156.517 (19)Ni2xvii—P1—Ni3i132.01 (5)
P4—Ni2—Ni2vii58.48 (2)Ni2xviii—P1—Ni3i69.59 (2)
Ni4x—Ni2—Ni2vii148.728 (6)Ni3ii—P1—Ni3i67.42 (4)
Ni2vi—Ni2—Ni2vii60.0P3xix—P2—Ni2115.40 (6)
P2—Ni2—Ni3vii55.154 (16)P3xix—P2—Ni3vi109.82 (3)
P1viii—Ni2—Ni3vii135.72 (4)Ni2—P2—Ni3vi70.27 (3)
P1ix—Ni2—Ni3vii55.45 (3)P3xix—P2—Ni3vii109.82 (3)
P4—Ni2—Ni3vii114.387 (15)Ni2—P2—Ni3vii70.27 (3)
Ni4x—Ni2—Ni3vii101.159 (17)Ni3vi—P2—Ni3vii132.81 (5)
Ni2vi—Ni2—Ni3vii60.956 (10)P3xix—P2—Ni1xx103.72 (5)
Ni2vii—Ni2—Ni3vii108.272 (11)Ni2—P2—Ni1xx127.79 (3)
P2—Ni2—Ni3vi55.154 (16)Ni3vi—P2—Ni1xx127.21 (4)
P1viii—Ni2—Ni3vi55.45 (3)Ni3vii—P2—Ni1xx64.601 (17)
P1ix—Ni2—Ni3vi135.72 (4)P3xix—P2—Ni1xxi103.72 (5)
P4—Ni2—Ni3vi114.387 (15)Ni2—P2—Ni1xxi127.79 (3)
Ni4x—Ni2—Ni3vi101.159 (17)Ni3vi—P2—Ni1xxi64.601 (17)
Ni2vi—Ni2—Ni3vi108.272 (11)Ni3vii—P2—Ni1xxi127.21 (4)
Ni2vii—Ni2—Ni3vi60.956 (10)Ni1xx—P2—Ni1xxi68.66 (3)
Ni3vii—Ni2—Ni3vi106.07 (3)P2xxii—P3—P2iii112.06 (4)
P2—Ni2—Ni1vi128.452 (16)P2xxii—P3—P2xxiii112.06 (4)
P1viii—Ni2—Ni1vi54.42 (3)P2iii—P3—P2xxiii112.06 (4)
P1ix—Ni2—Ni1vi132.50 (4)P2xxii—P3—Ni4106.74 (5)
P4—Ni2—Ni1vi56.477 (18)P2iii—P3—Ni4106.74 (5)
Ni4x—Ni2—Ni1vi90.295 (18)P2xxiii—P3—Ni4106.74 (5)
Ni2vi—Ni2—Ni1vi107.477 (12)Ni1vii—P4—Ni1vi118.209 (17)
Ni2vii—Ni2—Ni1vi61.138 (10)Ni1vii—P4—Ni1118.209 (17)
Ni3vii—Ni2—Ni1vi168.167 (17)Ni1vi—P4—Ni1118.209 (17)
Ni3vi—Ni2—Ni1vi74.184 (10)Ni1vii—P4—Ni266.01 (2)
P2—Ni2—Ni1vii128.452 (16)Ni1vi—P4—Ni266.01 (2)
P1viii—Ni2—Ni1vii132.50 (4)Ni1—P4—Ni2119.38 (6)
P1ix—Ni2—Ni1vii54.42 (3)Ni1vii—P4—Ni2vi66.01 (2)
P4—Ni2—Ni1vii56.477 (18)Ni1vi—P4—Ni2vi119.38 (6)
Ni4x—Ni2—Ni1vii90.295 (18)Ni1—P4—Ni2vi66.01 (2)
Ni2vi—Ni2—Ni1vii61.138 (10)Ni2—P4—Ni2vi63.04 (4)
Ni2vii—Ni2—Ni1vii107.477 (12)Ni1vii—P4—Ni2vii119.38 (6)
Ni3vii—Ni2—Ni1vii74.184 (10)Ni1vi—P4—Ni2vii66.01 (2)
Ni3vi—Ni2—Ni1vii168.167 (17)Ni1—P4—Ni2vii66.01 (2)
Ni1vi—Ni2—Ni1vii103.08 (3)Ni2—P4—Ni2vii63.04 (4)
P2vi—Ni3—P2vii86.67 (5)Ni2vi—P4—Ni2vii63.04 (4)
P2vi—Ni3—P1ii146.92 (3)Ni1vii—P4—Ni3xxiv113.93 (4)
P2vii—Ni3—P1ii85.63 (3)Ni1vi—P4—Ni3xxiv60.81 (2)
P2vi—Ni3—P1i85.63 (3)Ni1—P4—Ni3xxiv113.93 (4)
P2vii—Ni3—P1i146.92 (3)Ni2—P4—Ni3xxiv117.117 (13)
P1ii—Ni3—P1i83.52 (5)Ni2vi—P4—Ni3xxiv179.81 (5)
P2vi—Ni3—P4xi99.03 (3)Ni2vii—P4—Ni3xxiv117.117 (13)
P2vii—Ni3—P4xi99.03 (3)Ni1vii—P4—Ni3xxv60.81 (2)
P1ii—Ni3—P4xi113.95 (3)Ni1vi—P4—Ni3xxv113.93 (4)
P1i—Ni3—P4xi113.95 (3)Ni1—P4—Ni3xxv113.93 (4)
P2vi—Ni3—Ni1xi58.38 (3)Ni2—P4—Ni3xxv117.117 (13)
P2vii—Ni3—Ni1xi58.38 (3)Ni2vi—P4—Ni3xxv117.117 (13)
P1ii—Ni3—Ni1xi138.22 (3)Ni2vii—P4—Ni3xxv179.81 (5)
P1i—Ni3—Ni1xi138.22 (3)Ni3xxiv—P4—Ni3xxv62.73 (4)
P4xi—Ni3—Ni1xi58.58 (3)Ni1vii—P4—Ni3v113.93 (4)
P2vi—Ni3—Ni3ii103.30 (2)Ni1vi—P4—Ni3v113.93 (4)
P2vii—Ni3—Ni3ii156.41 (2)Ni1—P4—Ni3v60.81 (2)
P1ii—Ni3—Ni3ii96.374 (19)Ni2—P4—Ni3v179.81 (5)
P1i—Ni3—Ni3ii56.292 (19)Ni2vi—P4—Ni3v117.117 (13)
P4xi—Ni3—Ni3ii58.64 (2)Ni2vii—P4—Ni3v117.117 (13)
Ni1xi—Ni3—Ni3ii108.624 (10)Ni3xxiv—P4—Ni3v62.73 (4)
P2vi—Ni3—Ni3i156.41 (2)Ni3xxv—P4—Ni3v62.73 (4)
Symmetry codes: (i) y+1, xy, z; (ii) x+y+1, x+1, z; (iii) xy+1, x, z1/2; (iv) y, x+y, z1/2; (v) x+1, y+1, z1/2; (vi) x+y, x+1, z; (vii) y+1, xy+1, z; (viii) y, xy, z; (ix) x+y+1, x+2, z; (x) x, y+1, z; (xi) x+1, y+1, z+1/2; (xii) y, xy1, z; (xiii) x1, y, z; (xiv) x+y1, x, z; (xv) x, y1, z; (xvi) x+1, y, z; (xvii) y+2, xy+1, z; (xviii) x+y, x, z; (xix) x, y+1, z+1/2; (xx) y, x+y+1, z+1/2; (xxi) xy, x, z+1/2; (xxii) y1, x+y1, z1/2; (xxiii) x, y+1, z1/2; (xxiv) xy, x, z1/2; (xxv) y, x+y+1, z1/2.
 

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