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Haruhiko Morito, Takuji Ikeda, [Yukari Katsura](https://orcid.org/0000-0002-8905-2995), Hisanori Yamane

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[Na<sub>3</sub>MgB<sub>37</sub>Si<sub>9</sub>: an icosahedral B<sub>12</sub> cluster framework containing {Si<sub>8</sub>} units](https://mdr.nims.go.jp/datasets/cedf9359-2007-4870-89dd-86a318cd752f)

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Na3MgB37Si9: an icosa­hedral B12 cluster framework containing {Si8} unitsresearch communicationsActa Cryst. (2022). E78, 203–206 https://doi.org/10.1107/S2056989022000494 203Received 20 December 2021Accepted 13 January 2022Edited by W. T. A. Harrison, University ofAberdeen, ScotlandKeywords: crystal structure; boron-rich boride;sodium; silicon; single-crystal; B2O3 flux; crystalstructure; X-ray diffraction.CCDC reference: 2141726Supporting information: this article hassupporting information at journals.iucr.org/eNa3MgB37Si9: an icosahedral B12 cluster frameworkcontaining {Si8} unitsHaruhiko Morito,a* Takuji Ikeda,b Yukari Katsurac and Hisanori YamanedaInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan, bResearchInstitute for Chemical Process Technology, National Institute of Advanced Industrial Science and Technology, 4-2-1,Nigatake, Miyagino-ku, Sendai 983-8551, Japan, cNational Institute for Materials Science, 1-2-1 Sengen, Tsukuba,Ibaraki, 305-0047, Japan, and dInstitute of Multidisciplinary Research for Advanced Materials, Tohoku, University, 2-1-1Katahira, Aoba-ku, Sendai 980-8577, Japan. *Correspondence e-mail: haruhiko.morito.b5@tohoku.ac.jpSingle crystals of a novel sodium–magnesium boride silicide, Na3MgB37Si9 [a =10.1630 (3) Å, c = 16.5742 (6) Å, space group R3m (No. 166)], were synthesizedby heating a mixture of Na, Si and crystalline B with B2O3 flux in Mg vapor at1373 K. The Mg atoms in the title compound are located at an interstitial site ofthe Dy2.1B37Si9-type structure with an occupancy of 0.5. The (001) layers of B12icosahedra stack along the c-axis direction with shifting in the [–a/3, b/3, c/3]direction. A three-dimensional framework structure of the layers is formed viaB—Si bonds and {Si8} units of [Si]3—Si—Si—[Si]3.1. Chemical contextBoron-rich compounds composed of B12 icosahedral clustersare attracting attention as thermoelectric materials because oftheir low thermal conductivity resulting from their compli-cated crystal structures (Cahill et al., 1977). In our previousstudy, a novel ternary borosilicide, Na8B74.5Si17.5, was synthe-sized, and its crystal structure (Morito et al. 2010) and elec-tronic structure measured using soft X-ray spectrometry(Terauchi et al. 2018), have been reported. This compound hasa three-dimensional framework structure with layerscomposed of B12 icosahedral clusters and Si chains in thechannels of the B12 clusters. During the investigation of thiscompound, a new crystalline phase was synthesized in whichthe stacking sequence of the B12 cluster layers differed fromthat of Na8B74.5Si17.5. The composition analysis revealed thatthe new phase contained a small amount of Mg derived froman impurity in the starting material of amorphous B powder.Single crystals of this phase were prepared in the present studyby heating a starting mixture of Na, crystalline B, a flux ofB2O3 with Mg vapor, and the crystal structure was determinedusing single-crystal X-ray diffraction.2. Structural commentaryThe crystal structure of the new phase of compositionNa3MgB37Si9 is trigonal (space group R3m, No. 166), and thehexagonal lattice constants are a = 10.1630 (3) Å and c =16.5742 (6) Å. The structure is composed of B12 icosahedralclusters: the B—B distances of the 30 distinct bonds in thecluster are in the range of 1.791 (3)–1.843 (5) Å and theaverage distance is 1.811 Å (Table 1). The B12 icosahedralclusters are connected by a B2—B2 bond [1.761 (5) Å] on theISSN 2056-9890http://crossmark.crossref.org/dialog/?doi=10.1107/S2056989022000494&domain=pdf&date_stamp=2022-01-18(001) plane and form layers that stack along the c axis with asequence of ABCABC by shifts of [–a/3, b/3, c/3] (Figs. 1 and2).Six B12 units in the layers surround {Si8} units of composi-tion [Si2]3—Si3—Si3—[Si2]3. The bond lengths of 2.304 (3) Åfor Si3—Si3 and 2.3951 (9) Å for Si2—Si3 are comparablewith the bond length in crystalline silicon (2.35 Å). The bondangles of Si2—Si3—Si2 and Si2—Si3—Si3 are 113.86 (3)� and104.61 (4)�, respectively, which are distorted from the regulartetrahedral bond angle of 109.47�. The Si2—B1 distance is2.043 (2) Å, which is close to the Si—B distances (1.973–2.027 Å) found in �-silicon boride, SiB3 (Salvador et al. 2003).The framework structure of B12 icosahedra and {Si8} units ofthe title compound has also been reported in the structures ofMg3B36Si9C (Ludwig et al. 2013), RE1–xB12Si3.3–� (RE = Y, Gd–Lu) (0� x� 0.5, �� 0.3) (Zhang et al. 2003) and RE1-xB36Si9C(RE = Y, Gd–Lu) (Ludwig et al. 2013) with the same spacegroup of R3m. The {Si8} units with Si2—B4 bonds[2.082 (3) Å] and Si1/B5—Si1/B5 pairs that bind to the Batoms at B3 connect the B12 layers of Na3MgB37Si9 (Fig. 1).Because the Si1—Si1 distance of 1.460 (10) Å is short for anSi—Si bond and the B5—B5 distance 2.47 (4) Å is long for aB—B bond, it was concluded that disordered pairs of Si1—B5and B5—Si1 [B—Si = 1.96 (2) Å] are statistically present withequal occupancies. Similar disordered Si/B—Si/B pairs havebeen reported in Dy0.7B12.33Si3 (Si/B occupancy 0.5/0.5, Si—Blength = 1.838 Å; Zhang et al. 2003). Instead of Si/B—Si/Bpairs (Ludwig et al. 2013), Mg3B36Si9C contains Si/C—Si/Cpairs (Si/C occupancy 0.507/0.493, Si—C length = 1.881 Å).The Na1 site in the title compound is located around the{Si8} unit between the B12 cluster layers. The Na1—Si2distance is 2.8620 (4) Å and the Na1—B1 and Na1—B2distances are 2.811 (2) and 2.793 (2) Å, respectively. Thesedistances are almost the same as the Na—Si distance of Na4Si4[2.878 (3) Å; Morito et al., 2015] and Na—B distance of NaB15(2.798 Å; Naslain & Kasper, 1970). The Mg1 atom is situatedabove and below the {Si8} unit along the c-axis direction withan occupancy of 0.5. The Mg1—Si3 and Mg1—B2 distancesare 2.403 (4) Å and 2.333 (3) Å, respectively, which are closeto the Mg—Si (2.436 Å) and Mg—B distances (2.353 Å) inMgB12Si2 (Ludwig & Hillebrecht, 2006). The Na1—Mg1distance in the title compound is 3.0389 (9) Å, which is close tothe Na—Mg distance (3.120 Å) reported in Na4Mg4Sn3(Yamada et al. 2015). The site corresponding to the location ofMg1 in the title compound does not exist in Mg3B36Si9C(Ludwig et al. 2013), RE1-xB12Si3.3-� (RE = Y, Gd–Lu) (0 � x �0.5, � � 0.3) (Zhang et al. 2003) and RE1-xB36Si9C (RE = Y,Gd–Lu) (Ludwig et al. 2013).The number of electrons provided from Na and Mg to theframework of B37Si9 is five in Na3MgB37Si9. In relatedcompounds, the Mg atom in Mg3B36Si9C and the Dy atom inDy0.7B12.33Si3 (Dy2.1B37Si9) provide six and 6.3 electrons,respectively, and approximately six electrons are suppliedfrom RE in RE1–xB12Si3.3–� (RE = Y, Gd–Lu) (0 � x � 0.5,� � 0.3) and RE1–xB36Si9C (RE = Y, Gd–Lu). The latticeconstants and unit-cell volume of Mg3B36Si9C are a =10.0793 Å, c = 16.372 Å, and V = 1440.4 Å3 (Ludwig et al.204 Morito et al. � Na3MgB37Si9 Acta Cryst. (2022). E78, 203–206research communicationsFigure 2[110] projection of the crystal structure of Na3MgB37Si9.Figure 1Interconnection of B12 clusters, Si1/B5—Si1/B5 bonds, {Si8} units and Naand Mg atoms in Na3MgB37Si9. Displacement ellipsoids are drawn at the90% probability level. Symmetry codes: (i) x + 23, y + 13, z + 13; (ii) �x + 23,�y + 13,�z + 13; (iii)�x + y, 1� x, z; (iv) 1� y, 1 + x� y, z; (v) y� 13,�x + y+ 13, �z + 13; (vi) x � y + 23, x + 13, �z + 13; (vii) �x + 23, �y � 23, �z + 13; (viii)�x + 13,�y + 23,�z + 23; (ix) x + 13, y + 23, z� 13; (x)�y + 23, x� y + 13, z + 13; (xi)x� 13, y + 13, z + 13; (xii)�x + y + 23,�x + 43, z + 13; (xiii) 1� x + y, 1� x, z; (xiv)x, 1 + y, z; (xv)�y, x� y, z; (xvi) x� y + 13, x� 13,�z + 23; (xvii) y + 13,�x + y+ 23, �z + 23; (xviii) �x + 43, �y + 23, �z + 23.Table 1Selected geometric parameters (Å, �).Na1—B2i 2.793 (2) B2—B2viii 1.761 (5)Na1—B1 2.811 (2) B3—B5i 1.689 (7)Na1—Si2i 2.8621 (4) B3—Si1i 1.888 (4)Na1—B4i 2.9605 (16) B4—Si2 2.082 (3)Mg1—B2ii 2.333 (3) B5—B3iii 1.689 (7)B1—B3iii 1.791 (3) B5—Si1ix 1.96 (2)B1—B2iv 1.798 (3) B5—B5ix 2.47 (4)B1—B1v 1.806 (4) Si1—Si1ix 1.460 (10)B1—B2vi 1.813 (3) Si2—Si3x 2.3951 (9)B1—B4vii 1.815 (3) Si3—Si3xi 2.304 (3)B1—Si2i 2.043 (2)Si3xi—Si3—Si2x 104.62 (4) Si2x—Si3—Si2xii 113.86 (3)Symmetry codes: (i) �xþ 23;�yþ 13;�zþ 13; (ii) �y; x� y; z; (iii)x� y� 13; x� 23;�zþ 13; (iv) x� yþ 23;�yþ 13;�zþ 13; (v) �xþ 23;�xþ yþ 13;�z þ 13;(vi) �x þ y;�x; z; (vii) �xþ yþ 13;�xþ 23; z� 13; (viii) �xþ y; y; z; (ix) �x;�y;�z; (x)�xþ 13;�yþ 23;�zþ 23; (xi) �x;�y;�z þ 1; (xii) y� 23;�xþ y � 13;�zþ 23.2013), those of RE1–xB12Si3.3–� (RE = Y, Gd–Lu) (0 � x � 0.5,�� 0.3) are a = 10.046–10.095 Å, c = 16.298–16.467 Å, and V =1429–1454 Å3 (Zhang et al. 2003) and those of RE1–xB36Si9C(RE = Y, Gd–Lu) are a = 10.000–10.096 Å, c = 16.225–16.454 Å, and V = 1405–1452 Å3 (Ludwig et al. 2013). Thus, itmay be seen that the lattice constants of Na3MgB37Si9 arelarger than those of related compounds and the unit-cellvolume of Na3MgB37Si9 is approximately 2% larger than themaximum unit-cell volume of 1454 Å3 for the RE1–xB12Si3.3–�series with RE = Yb (Zhang et al. 2003). This increase in thelattice constants could be related to the occupancy of the Mg1site, which is not found in other compounds.Table 2 compares the interatomic distances forNa3MgB37Si9, Dy2.1B37Si9 and Mg3B36Si9C. The average B—Bdistances of B12 icosahedra, B2—B2 distances between clus-ters, and Si2—B4 distances for Na3MgB37Si9 are longer thanthose of other compounds. However, only the bond distance ofSi3—Si3, in which Si3 only binds to Si, is specifically shorter. Itis assumed that this bond became shorter because of anincrease in the bond order from 1 because of a decrease in thenumber of electrons in the antibonding orbitals of the Si3—Si3unit with a decrease in the electron count for the entireframework. Assuming that the main cause of the latticeexpansion of Na3MgB37Si9 is a decrease in the bonding forcebetween B—B and B—Si atoms because of electron deficiencyin the bonding orbitals of the B37Si9 framework, the latticeconstant can be reduced by increasing the Mg occupancy,which can be attained by increasing the Mg vapor pressureduring the synthesis.3. Database surveyIn space group R3m, the framework structures of B12 icosa-hedral clusters containing {Si8} units similar to Na3MgB37Si9have been reported for Mg3B36Si9C (Ludwig et al. 2013),RE1–xB12Si3.3–� (RE = Y, Gd–Lu) (0 � x � 0.5, � �0.3) (Zhanget al. 2003) and RE1–xB36Si9C (RE = Y, Gd–Lu) (Ludwig et al.2013).4. Synthesis and crystallizationNa metal pieces (purity 99.95%, Nippon Soda Co., Ltd.),crystalline B powder (99.9%, FUJIFILM Wako Pure ChemicalIndustries Co., Ltd.) and Si powder (99.999%, KojundoChemical Lab. Co., Ltd.) were weighed in a BN crucible(99.5%, Showa Denko K. K., outer diameter = 8.5 mm, innerdiameter = 6.5 mm, depth = 18 mm), with a molar ratio ofNa:B:Si = 5:4:3 (a total weight 280 mg) in a high-purity Ar-filled glove box (O2 < 1 ppm, H2O < 1 ppm). Then, 10 mg ofB2O3 powder (90%, FUJIFILM Wako Pure Chemical Indus-tries, Ltd.) were added to the crucible, which was stacked onanother BN crucible containing 30 mg of Mg powder (99.9%,rare metallic), and these crucibles were encapsulated in astainless steel container (SUS316, outer diameter = 12.7 mm,inner diameter = 10.75 mm, length 80 mm) with Ar gas. Thecontainer was heated at 1373 K for 24 h using an electricfurnace. After cooling, the crucible was taken out from thereaction container, and any Na and NaSi remaining in thecrucible were reacted and removed with 2-propanol andethanol. Then, the sample was washed with pure water toremove water-soluble compounds such as sodium borate andalkoxide produced by the reaction of Na and alcohol to leaveblack plates of the title compound. An electron probemicroanalyzer (EPMA; JEOL Ltd., JXA-8200) was used toanalyze the composition of the obtained single crystal as Naresearch communicationsActa Cryst. (2022). E78, 203–206 Morito et al. � Na3MgB37Si9 205Table 2Cell parameters (Å), cell volumes (Å3) and selected bond lengths (Å) ofNa3MgB37Si9, Dy2.1B37Si9a and Mg3B36Si9C.Na3MgB37Si9 Dy2.1B37Si9 Mg3B36Si9Ca 10.1630 (3) 10.078 10.079c 16.5742 (6) 16.465 16.372V 1482.54 (10) 1448.3 1440.4B—Bav of B12 icosahedron 1.811 1.805 1.798B2—B2 1.761 (5) 1.738 1.738Si1—B3 1.887 (4) 1.877 1.851Si1—B5/C 1.96 (2) 1.84 1.88Si2—B1 2.043 (2) 2.032 2.035Si2—B4 2.082 (3) 2.053 2.038Si3—Si2 2.3951 (9) 2.366 2.362Si3—Si3 2.304 (3) 2.343 2.341Na1—B1 2.811 (2) 2.794 2.792Na1—B2 2.793 (2) 2.751 2.729Na1—B4 2.9604 (16) 2.934 2.934Na1—Si2 2.8620 (4) 2.835 2.832Mg1—B2 2.333 (3)Mg1—B4 2.568 (3)Mg1—Si3 2.403 (4)Notes: (a) Zhang et al. (2003); (b) Ludwig et al. (2013).Table 3Experimental details.Crystal dataChemical formula Na3MgB37Si9Mr 746.06Crystal system, space group Trigonal, R3mTemperature (K) 298a, c (Å) 10.1630 (3), 16.5742 (6)V (Å3) 1482.54 (10)Z 3Radiation type Mo K�� (mm�1) 0.72Crystal size (mm) 0.20 � 0.16 � 0.02Data collectionDiffractometer Burker, D8 QUESTAbsorption correction Multi-scan (SADABS; Bruker,2018)Tmin, Tmax 0.911, 1.000No. of measured, independent andobserved [I > 2�(I)] reflections8352, 562, 540Rint 0.032(sin �/�)max (Å�1) 0.703RefinementR[F 2 > 2�(F 2)], wR(F 2), S 0.035, 0.076, 1.31No. of reflections 562No. of parameters 57� max, � min (e Å�3) 0.58, �0.53Computer programs: APEX3 and SAINT (Bruker, 2018), SHELXT2014/5 (Sheldrick,2015a), SHELXL2014/7 (Sheldrick, 2015b), VESTA (Momma & Izumi, 2011) andpublCIF (Westrip, 2010).5.49 (8), Mg 2.37 (7), B 74.8 (7), Si 17.3 (4) atom %, which isnearly matched by Na3MgB37Si9 (Na 6.0, Mg 2.0, B 74.0, Si18.0 atom %). Other elements such as O were not found.5. RefinementCrystal data, data collection and structure refinement detailsare summarized in Table 3. The occupancy of the Mg1 site inthe analysis of the initial model was 0.506 (10), whereas theoccupancy of the B5 and Si1 sites was 0.519 (15) and 0.481,respectively. These occupancies were fixed at 0.5, and thecomposition formula was determined to be Na3MgB37Si9. Thecrystal structure was refined by considering (001) twinning,which reduced the R-value (all data) from 0.0651 to 0.0380.AcknowledgementsWe thank T. Kamaya for his help with the EPMA analysis.Funding informationFunding for this research was provided by: the Japan Scienceand Technology Agency (JST) CREST (grant No.JPMJCR19J1).ReferencesBruker (2018). APEX3, SAINT and SADABS. Bruker AXS inc.,Madison, Wisconsin, USA.Cahill, D. G., Fischer, H. E., Watson, S. K., Pohl, R. O. & Slack, G. A.(1989). Phys. Rev. B, 40, 3254–3260.Ludwig, T. & Hillebrecht, H. (2006). J. Solid State Chem. 179, 1623–1629.Ludwig, T., Pediaditakis, A., Sagawe, V. & Hillebrecht, H. (2013). J.Solid State Chem. 204, 113–122.Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276.Morito, H., Eck, B., Dronskowski, R. & Yamane, H. (2010). DaltonTrans. 39, 10197–10202.Morito, H., Momma, K. & Yamane, H. (2015). J. Alloys Compd. 623,473–479.Naslain, R. & Kasper, J. S. (1970). J. Solid State Chem. 1, 150–151.Salvador, J. R., Bilc, D., Mahanti, S. D. & Kanatzidis, M. G. (2003).Angew. Chem. Int. Ed. 42, 1929–1932.Sheldrick, G. M. (2015a). Acta Cryst. A71, 3–8.Sheldrick, G. M. (2015b). Acta Cryst. C71, 3–8.Terauchi, M., Morito, H., Yamane, H., Koshiya, S. & Kimoto, K.(2018). Microscopy, 67, i72–i77.Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925.Yamada, T., Ishiyama, R. & Yamane, H. (2015). Jpn. J. Appl. Phys. 54,07J, C04.Zhang, F. X., Xu, F. F., Mori, T., Liu, Q. L. & Tanaka, T. (2003). J.Solid State Chem. 170, 75–81.206 Morito et al. � Na3MgB37Si9 Acta Cryst. (2022). E78, 203–206research communicationshttp://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB1http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB1http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB2http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB2http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB3http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB3http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB4http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB4http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB5http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB6http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB6http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB17http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB17http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB8http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB9http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB9http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB10http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB11http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB12http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB12http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB13http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB14http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB14http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB15http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdfbb&cnor=hb8005&bbid=BB15supporting informationsup-1Acta Cryst. (2022). E78, 203-206    supporting informationActa Cryst. (2022). E78, 203-206    [https://doi.org/10.1107/S2056989022000494]Na3MgB37Si9: an icosahedral B12 cluster framework containing {Si8} unitsHaruhiko Morito, Takuji Ikeda, Yukari Katsura and Hisanori YamaneComputing details Data collection: Instrument Service (Bruker, 2018); cell refinement: APEX3 (Bruker, 2018); data reduction: SAINT (Bruker, 2018); program(s) used to solve structure: SHELXT2014/5 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2015b); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).3 sodium 1 magnesium 37 boron 9 silicon Crystal data Na3MgB37Si9Mr = 746.06Trigonal, R3ma = 10.1630 (3) Åc = 16.5742 (6) ÅV = 1482.54 (10) Å3Z = 3F(000) = 1068Dx = 2.507 Mg m−3Mo Kα radiation, λ = 0.71073 ÅCell parameters from 6032 reflectionsθ = 3.7–41.2°µ = 0.72 mm−1T = 298 KPlate, black0.20 × 0.16 × 0.02 mmData collection Burker, D8 QUEST diffractometerDetector resolution: 10 pixels mm-1ω scansAbsorption correction: multi-scan (SADABS; Bruker, 2018)Tmin = 0.911, Tmax = 1.0008352 measured reflections562 independent reflections540 reflections with I > 2σ(I)Rint = 0.032θmax = 30.0°, θmin = 2.6°h = −14→14k = −14→14l = −23→22Refinement Refinement on F2Least-squares matrix: fullR[F2 > 2σ(F2)] = 0.035wR(F2) = 0.076S = 1.31562 reflections57 parameters0 restraintsw = 1/[σ2(Fo2) + 11.3797P] where P = (Fo2 + 2Fc2)/3(Δ/σ)max < 0.001Δρmax = 0.58 e Å−3Δρmin = −0.53 e Å−3Extinction correction: SHELXL2014/7 (Sheldrick 2015), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4Extinction coefficient: 0.0030 (6)supporting informationsup-2Acta Cryst. (2022). E78, 203-206    Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.Refinement. Refined as a 2-component inversion twin.Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) x y z Uiso*/Ueq Occ. (<1)Na1 0.5000 0.0000 0.0000 0.0179 (5)Mg1 0.0000 0.0000 0.2855 (2) 0.0074 (7) 0.5B1 0.3002 (3) 0.0065 (2) 0.11511 (13) 0.0064 (4)B2 0.0027 (3) 0.1787 (3) 0.19610 (13) 0.0072 (4)B3 0.7591 (2) 0.2409 (2) 0.2315 (2) 0.0116 (7)B4 0.47839 (19) 0.52161 (19) 0.39743 (19) 0.0079 (6)B5 0.0000 0.0000 0.0744 (12) 0.026 (5) 0.5Si1 0.0000 0.0000 0.0441 (3) 0.0103 (9) 0.5Si2 0.46499 (5) 0.53501 (5) 0.27264 (5) 0.0056 (2)Si3 0.0000 0.0000 0.43049 (10) 0.0120 (3)Atomic displacement parameters (Å2) U11 U22 U33 U12 U13 U23Na1 0.0137 (7) 0.0265 (11) 0.0178 (8) 0.0132 (6) 0.0027 (4) 0.0054 (8)Mg1 0.0060 (9) 0.0060 (9) 0.0102 (15) 0.0030 (5) 0.000 0.000B1 0.0064 (9) 0.0041 (9) 0.0080 (8) 0.0020 (8) −0.0004 (7) 0.0001 (8)B2 0.0054 (9) 0.0053 (9) 0.0102 (9) 0.0022 (8) −0.0005 (8) −0.0009 (8)B3 0.0087 (10) 0.0087 (10) 0.0116 (13) 0.0001 (12) 0.0035 (7) −0.0035 (7)B4 0.0050 (9) 0.0050 (9) 0.0116 (13) 0.0009 (11) −0.0004 (6) 0.0004 (6)B5 0.033 (8) 0.033 (8) 0.012 (9) 0.017 (4) 0.000 0.000Si1 0.0061 (11) 0.0061 (11) 0.019 (3) 0.0031 (5) 0.000 0.000Si2 0.0044 (3) 0.0044 (3) 0.0073 (4) 0.0015 (3) 0.00040 (14) −0.00040 (14)Si3 0.0055 (4) 0.0055 (4) 0.0249 (8) 0.0028 (2) 0.000 0.000Geometric parameters (Å, º) Na1—B2i 2.793 (2) B3—Si1i 1.888 (4)Na1—B2ii 2.793 (2) B3—B5xxx 3.343 (19)Na1—B2iii 2.793 (2) B3—Na1xxx 4.123 (3)Na1—B2iv 2.793 (2) B3—Na1xxxi 4.123 (3)Na1—B1v 2.811 (2) B3—Na1xxxii 4.605 (3)Na1—B1vi 2.811 (2) B4—B3xxviii 1.799 (5)Na1—B1vii 2.811 (2) B4—B1xxxiii 1.815 (3)Na1—B1 2.811 (2) B4—B1xxxiv 1.815 (3)Na1—Si2viii 2.8620 (4) B4—B2xxxv 1.824 (4)Na1—Si2ix 2.8620 (4) B4—B2xv 1.824 (4)Na1—Si2i 2.8621 (4) B4—Si2 2.082 (3)supporting informationsup-3Acta Cryst. (2022). E78, 203-206    Na1—Si2ii 2.8621 (4) B4—Mg1xv 2.568 (3)Na1—B4viii 2.9604 (16) B4—Na1xxiv 2.9605 (16)Na1—B4ix 2.9604 (16) B4—Na1xxxiii 2.9605 (16)Na1—B4i 2.9605 (16) B4—B5xxx 3.319 (3)Na1—B4ii 2.9605 (16) B4—B5i 4.031 (12)Na1—Mg1i 3.0389 (9) B4—B5xv 4.117 (16)Na1—Mg1ii 3.0389 (9) B5—Si1 0.503 (18)Mg1—B2x 2.333 (3) B5—B3xviii 1.689 (7)Mg1—B2xi 2.333 (3) B5—B3xxxvi 1.689 (7)Mg1—B2xii 2.333 (3) B5—B3i 1.689 (7)Mg1—B2xiii 2.333 (3) B5—Si1xxi 1.96 (2)Mg1—B2xiv 2.333 (3) B5—B5xxi 2.47 (4)Mg1—B2 2.333 (3) B5—B2xiii 2.705 (16)Mg1—Si3 2.403 (4) B5—B2xiv 2.705 (16)Mg1—B4xv 2.568 (3) B5—B2xi 2.705 (16)Mg1—B4xvi 2.568 (3) B5—B2xii 2.705 (16)Mg1—B4xvii 2.568 (3) B5—B2x 2.705 (16)Mg1—Si2xv 2.933 (2) Si1—Si1xxi 1.460 (10)Mg1—Si2xvii 2.933 (2) Si1—B3xviii 1.887 (4)B1—B3xviii 1.791 (3) Si1—B3xxxvi 1.887 (4)B1—B2iv 1.798 (3) Si1—B3i 1.888 (4)B1—B1xix 1.806 (4) Si1—B5xxi 1.96 (2)B1—B2xiv 1.813 (3) Si1—Na1xiv 5.1337 (7)B1—B4ix 1.815 (3) Si1—Na1xxii 5.1337 (7)B1—Si2i 2.043 (2) Si1—Na1xxxvii 5.1337 (7)B1—B5 3.093 (5) Si1—Na1xxxviii 5.1337 (7)B1—Na1xx 3.954 (2) Si1—Na1x 5.1337 (7)B1—B5i 4.268 (12) Si2—B1i 2.043 (2)B1—B5xxi 4.356 (15) Si2—B1xxix 2.043 (2)B1—Na1xxii 4.768 (2) Si2—Si3xv 2.3951 (9)B2—B2xiii 1.761 (5) Si2—Na1xxxiii 2.8621 (4)B2—B1xxiii 1.798 (3) Si2—Na1xxiv 2.8621 (4)B2—B1x 1.813 (3) Si2—Mg1xv 2.933 (2)B2—B3i 1.816 (4) Si2—B5i 3.5572 (16)B2—B4xv 1.824 (4) Si2—B5xxx 4.197 (11)B2—B2xi 1.843 (5) Si2—Na1xxii 4.5605 (8)B2—B5 2.705 (16) Si2—Na1xxxix 5.3470 (8)B2—Na1xxiv 2.793 (2) Si3—Si3xl 2.304 (3)B2—Na1xxv 4.143 (2) Si3—Si2xv 2.3951 (9)B2—B5xxvi 4.537 (5) Si3—Si2xvi 2.3952 (9)B2—Na1x 4.617 (2) Si3—Si2xvii 2.3952 (9)B3—B5i 1.689 (7) Si3—Na1xx 3.3466 (8)B3—B1xxvii 1.791 (3) Si3—Na1xxv 3.3467 (8)B3—B1iv 1.791 (3) Si3—Na1xxiv 3.3467 (8)B3—B4xxviii 1.799 (5) Si3—Na1xli 4.8918 (14)B3—B2i 1.816 (4) Si3—Na1xlii 4.8918 (14)B3—B2xxix 1.816 (4) Si3—Na1xliii 4.8918 (14)supporting informationsup-4Acta Cryst. (2022). E78, 203-206    B2i—Na1—B2ii 180.00 (5) B1iv—B3—B2xxix 60.33 (12)B2i—Na1—B2iii 143.25 (9) B4xxviii—B3—B2xxix 109.8 (2)B2ii—Na1—B2iii 36.75 (9) B2i—B3—B2xxix 60.99 (18)B2i—Na1—B2iv 36.75 (9) B5i—B3—Si1i 14.9 (6)B2ii—Na1—B2iv 143.25 (9) B1xxvii—B3—Si1i 123.43 (12)B2iii—Na1—B2iv 180.00 (11) B1iv—B3—Si1i 123.43 (12)B2i—Na1—B1v 109.34 (7) B4xxviii—B3—Si1i 129.2 (2)B2ii—Na1—B1v 70.66 (7) B2i—B3—Si1i 113.5 (2)B2iii—Na1—B1v 37.43 (6) B2xxix—B3—Si1i 113.5 (2)B2iv—Na1—B1v 142.57 (6) B5i—B3—B5xxx 45.3 (8)B2i—Na1—B1vi 37.43 (6) B1xxvii—B3—B5xxx 112.55 (16)B2ii—Na1—B1vi 142.57 (6) B1iv—B3—B5xxx 112.55 (16)B2iii—Na1—B1vi 109.34 (7) B4xxviii—B3—B5xxx 98.8 (3)B2iv—Na1—B1vi 70.66 (7) B2i—B3—B5xxx 136.96 (19)B1v—Na1—B1vi 85.53 (9) B2xxix—B3—B5xxx 136.96 (19)B2i—Na1—B1vii 142.57 (6) Si1i—B3—B5xxx 30.4 (3)B2ii—Na1—B1vii 37.43 (6) B5i—B3—Na1xxx 122.5 (5)B2iii—Na1—B1vii 70.66 (7) B1xxvii—B3—Na1xxx 99.85 (16)B2iv—Na1—B1vii 109.34 (7) B1iv—B3—Na1xxx 33.59 (11)B1v—Na1—B1vii 94.47 (9) B4xxviii—B3—Na1xxx 39.37 (5)B1vi—Na1—B1vii 180.00 (6) B2i—B3—Na1xxx 133.94 (17)B2i—Na1—B1 70.66 (7) B2xxix—B3—Na1xxx 93.92 (11)B2ii—Na1—B1 109.34 (7) Si1i—B3—Na1xxx 111.86 (14)B2iii—Na1—B1 142.57 (6) B5xxx—B3—Na1xxx 88.28 (16)B2iv—Na1—B1 37.43 (6) B5i—B3—Na1xxxi 122.5 (5)B1v—Na1—B1 180.0 B1xxvii—B3—Na1xxxi 33.59 (11)B1vi—Na1—B1 94.47 (9) B1iv—B3—Na1xxxi 99.85 (16)B1vii—Na1—B1 85.53 (9) B4xxviii—B3—Na1xxxi 39.37 (5)B2i—Na1—Si2viii 78.17 (5) B2i—B3—Na1xxxi 93.92 (11)B2ii—Na1—Si2viii 101.83 (5) B2xxix—B3—Na1xxxi 133.94 (17)B2iii—Na1—Si2viii 76.28 (5) Si1i—B3—Na1xxxi 111.86 (14)B2iv—Na1—Si2viii 103.72 (5) B5xxx—B3—Na1xxxi 88.28 (16)B1v—Na1—Si2viii 73.21 (5) Na1xxx—B3—Na1xxxi 76.09 (7)B1vi—Na1—Si2viii 42.21 (5) B5i—B3—Na1 101.0 (6)B1vii—Na1—Si2viii 137.79 (5) B1xxvii—B3—Na1 57.83 (11)B1—Na1—Si2viii 106.79 (5) B1iv—B3—Na1 111.50 (15)B2i—Na1—Si2ix 101.83 (5) B4xxviii—B3—Na1 108.78 (14)B2ii—Na1—Si2ix 78.17 (5) B2i—B3—Na1 3.02 (8)B2iii—Na1—Si2ix 103.72 (5) B2xxix—B3—Na1 63.98 (11)B2iv—Na1—Si2ix 76.28 (5) Si1i—B3—Na1 113.12 (15)B1v—Na1—Si2ix 106.79 (5) B5xxx—B3—Na1 135.32 (13)B1vi—Na1—Si2ix 137.79 (5) Na1xxx—B3—Na1 134.78 (8)B1vii—Na1—Si2ix 42.21 (5) Na1xxxi—B3—Na1 91.40 (4)B1—Na1—Si2ix 73.21 (5) B5i—B3—Na1xxxii 101.0 (6)Si2viii—Na1—Si2ix 180.00 (3) B1xxvii—B3—Na1xxxii 111.50 (15)B2i—Na1—Si2i 103.71 (5) B1iv—B3—Na1xxxii 57.83 (11)B2ii—Na1—Si2i 76.29 (5) B4xxviii—B3—Na1xxxii 108.78 (14)B2iii—Na1—Si2i 101.83 (5) B2i—B3—Na1xxxii 63.98 (11)supporting informationsup-5Acta Cryst. (2022). E78, 203-206    B2iv—Na1—Si2i 78.17 (5) B2xxix—B3—Na1xxxii 3.02 (8)B1v—Na1—Si2i 137.79 (5) Si1i—B3—Na1xxxii 113.12 (15)B1vi—Na1—Si2i 106.80 (5) B5xxx—B3—Na1xxxii 135.32 (13)B1vii—Na1—Si2i 73.20 (5) Na1xxx—B3—Na1xxxii 91.40 (4)B1—Na1—Si2i 42.21 (5) Na1xxxi—B3—Na1xxxii 134.78 (8)Si2viii—Na1—Si2i 89.06 (3) Na1—B3—Na1xxxii 66.97 (5)Si2ix—Na1—Si2i 90.94 (3) B3xxviii—B4—B1xxxiii 59.41 (12)B2i—Na1—Si2ii 76.29 (5) B3xxviii—B4—B1xxxiv 59.41 (12)B2ii—Na1—Si2ii 103.71 (5) B1xxxiii—B4—B1xxxiv 107.0 (2)B2iii—Na1—Si2ii 78.17 (5) B3xxviii—B4—B2xxxv 106.60 (19)B2iv—Na1—Si2ii 101.83 (5) B1xxxiii—B4—B2xxxv 59.22 (12)B1v—Na1—Si2ii 42.21 (5) B1xxxiv—B4—B2xxxv 107.49 (19)B1vi—Na1—Si2ii 73.20 (5) B3xxviii—B4—B2xv 106.60 (19)B1vii—Na1—Si2ii 106.80 (5) B1xxxiii—B4—B2xv 107.49 (19)B1—Na1—Si2ii 137.79 (5) B1xxxiv—B4—B2xv 59.22 (12)Si2viii—Na1—Si2ii 90.94 (3) B2xxxv—B4—B2xv 60.69 (17)Si2ix—Na1—Si2ii 89.06 (3) B3xxviii—B4—Si2 116.8 (2)Si2i—Na1—Si2ii 180.00 (3) B1xxxiii—B4—Si2 120.31 (12)B2i—Na1—B4viii 109.24 (8) B1xxxiv—B4—Si2 120.31 (12)B2ii—Na1—B4viii 70.76 (8) B2xxxv—B4—Si2 126.71 (16)B2iii—Na1—B4viii 36.82 (8) B2xv—B4—Si2 126.71 (16)B2iv—Na1—B4viii 143.18 (8) B3xxviii—B4—Mg1xv 165.7 (2)B1v—Na1—B4viii 36.55 (7) B1xxxiii—B4—Mg1xv 114.65 (14)B1vi—Na1—B4viii 72.94 (8) B1xxxiv—B4—Mg1xv 114.65 (14)B1vii—Na1—B4viii 107.06 (8) B2xxxv—B4—Mg1xv 61.46 (13)B1—Na1—B4viii 143.45 (7) B2xv—B4—Mg1xv 61.46 (13)Si2viii—Na1—B4viii 41.86 (6) Si2—B4—Mg1xv 77.46 (13)Si2ix—Na1—B4viii 138.14 (6) B3xxviii—B4—Na1xxiv 117.95 (7)Si2i—Na1—B4viii 107.63 (6) B1xxxiii—B4—Na1xxiv 173.12 (16)Si2ii—Na1—B4viii 72.37 (6) B1xxxiv—B4—Na1xxiv 67.24 (8)B2i—Na1—B4ix 70.76 (8) B2xxxv—B4—Na1xxiv 118.03 (15)B2ii—Na1—B4ix 109.24 (8) B2xv—B4—Na1xxiv 66.59 (8)B2iii—Na1—B4ix 143.18 (8) Si2—B4—Na1xxiv 66.54 (6)B2iv—Na1—B4ix 36.82 (8) Mg1xv—B4—Na1xxiv 66.25 (7)B1v—Na1—B4ix 143.45 (7) B3xxviii—B4—Na1xxxiii 117.95 (7)B1vi—Na1—B4ix 107.06 (8) B1xxxiii—B4—Na1xxxiii 67.24 (8)B1vii—Na1—B4ix 72.94 (8) B1xxxiv—B4—Na1xxxiii 173.12 (16)B1—Na1—B4ix 36.55 (7) B2xxxv—B4—Na1xxxiii 66.59 (8)Si2viii—Na1—B4ix 138.14 (6) B2xv—B4—Na1xxxiii 118.03 (15)Si2ix—Na1—B4ix 41.86 (6) Si2—B4—Na1xxxiii 66.54 (6)Si2i—Na1—B4ix 72.37 (6) Mg1xv—B4—Na1xxxiii 66.25 (7)Si2ii—Na1—B4ix 107.63 (6) Na1xxiv—B4—Na1xxxiii 118.24 (11)B4viii—Na1—B4ix 180.00 (18) B3xxviii—B4—B5xxx 17.4 (4)B2i—Na1—B4i 143.17 (8) B1xxxiii—B4—B5xxx 66.8 (2)B2ii—Na1—B4i 36.83 (8) B1xxxiv—B4—B5xxx 66.8 (2)B2iii—Na1—B4i 70.76 (8) B2xxxv—B4—B5xxx 121.1 (3)B2iv—Na1—B4i 109.24 (8) B2xv—B4—B5xxx 121.1 (3)B1v—Na1—B4i 107.06 (8) Si2—B4—B5xxx 99.4 (4)supporting informationsup-6Acta Cryst. (2022). E78, 203-206    B1vi—Na1—B4i 143.45 (7) Mg1xv—B4—B5xxx 176.9 (4)B1vii—Na1—B4i 36.55 (7) Na1xxiv—B4—B5xxx 112.64 (15)B1—Na1—B4i 72.94 (8) Na1xxxiii—B4—B5xxx 112.64 (15)Si2viii—Na1—B4i 107.63 (6) B3xxviii—B4—B5i 55.0 (3)Si2ix—Na1—B4i 72.37 (6) B1xxxiii—B4—B5i 87.8 (2)Si2i—Na1—B4i 41.85 (6) B1xxxiv—B4—B5i 87.8 (2)Si2ii—Na1—B4i 138.15 (6) B2xxxv—B4—B5i 146.20 (15)B4viii—Na1—B4i 96.65 (12) B2xv—B4—B5i 146.20 (15)B4ix—Na1—B4i 83.35 (12) Si2—B4—B5i 61.8 (3)B2i—Na1—B4ii 36.83 (8) Mg1xv—B4—B5i 139.3 (3)B2ii—Na1—B4ii 143.17 (8) Na1xxiv—B4—B5i 95.59 (14)B2iii—Na1—B4ii 109.24 (8) Na1xxxiii—B4—B5i 95.59 (14)B2iv—Na1—B4ii 70.76 (8) B5xxx—B4—B5i 37.6 (6)B1v—Na1—B4ii 72.94 (8) B3xxviii—B4—B5xv 108.0 (2)B1vi—Na1—B4ii 36.55 (7) B1xxxiii—B4—B5xv 82.20 (16)B1vii—Na1—B4ii 143.45 (7) B1xxxiv—B4—B5xv 82.20 (16)B1—Na1—B4ii 107.06 (8) B2xxxv—B4—B5xv 30.37 (9)Si2viii—Na1—B4ii 72.37 (6) B2xv—B4—B5xv 30.37 (9)Si2ix—Na1—B4ii 107.63 (6) Si2—B4—B5xv 135.2 (2)Si2i—Na1—B4ii 138.15 (6) Mg1xv—B4—B5xv 57.7 (2)Si2ii—Na1—B4ii 41.85 (6) Na1xxiv—B4—B5xv 93.09 (12)B4viii—Na1—B4ii 83.35 (12) Na1xxxiii—B4—B5xv 93.09 (12)B4ix—Na1—B4ii 96.65 (12) B5xxx—B4—B5xv 125.4 (2)B4i—Na1—B4ii 180.00 (13) B5i—B4—B5xv 163.0 (4)B2i—Na1—Mg1i 46.93 (7) Si1—B5—B3xviii 105.6 (7)B2ii—Na1—Mg1i 133.07 (7) Si1—B5—B3xxxvi 105.6 (7)B2iii—Na1—Mg1i 133.07 (7) B3xviii—B5—B3xxxvi 113.0 (6)B2iv—Na1—Mg1i 46.93 (7) Si1—B5—B3i 105.6 (7)B1v—Na1—Mg1i 101.34 (6) B3xviii—B5—B3i 113.0 (6)B1vi—Na1—Mg1i 78.66 (6) B3xxxvi—B5—B3i 113.0 (6)B1vii—Na1—Mg1i 101.34 (6) Si1—B5—Si1xxi 0.0B1—Na1—Mg1i 78.65 (6) B3xviii—B5—Si1xxi 105.6 (7)Si2viii—Na1—Mg1i 120.47 (4) B3xxxvi—B5—Si1xxi 105.6 (7)Si2ix—Na1—Mg1i 59.53 (4) B3i—B5—Si1xxi 105.6 (7)Si2i—Na1—Mg1i 120.47 (4) Si1—B5—B5xxi 0.000 (1)Si2ii—Na1—Mg1i 59.53 (4) B3xviii—B5—B5xxi 105.6 (7)B4viii—Na1—Mg1i 129.34 (6) B3xxxvi—B5—B5xxi 105.6 (7)B4ix—Na1—Mg1i 50.66 (6) B3i—B5—B5xxi 105.6 (7)B4i—Na1—Mg1i 129.34 (6) Si1xxi—B5—B5xxi 0.0B4ii—Na1—Mg1i 50.66 (6) Si1—B5—B2 138.2 (3)B2i—Na1—Mg1ii 133.07 (7) B3xviii—B5—B2 77.9 (5)B2ii—Na1—Mg1ii 46.93 (7) B3xxxvi—B5—B2 111.0 (9)B2iii—Na1—Mg1ii 46.93 (7) B3i—B5—B2 41.2 (4)B2iv—Na1—Mg1ii 133.07 (7) Si1xxi—B5—B2 138.2 (3)B1v—Na1—Mg1ii 78.66 (6) B5xxi—B5—B2 138.2 (3)B1vi—Na1—Mg1ii 101.34 (6) Si1—B5—B2xiii 138.2 (3)B1vii—Na1—Mg1ii 78.66 (6) B3xviii—B5—B2xiii 41.2 (4)B1—Na1—Mg1ii 101.35 (6) B3xxxvi—B5—B2xiii 111.1 (9)supporting informationsup-7Acta Cryst. (2022). E78, 203-206    Si2viii—Na1—Mg1ii 59.53 (4) B3i—B5—B2xiii 77.9 (5)Si2ix—Na1—Mg1ii 120.47 (4) Si1xxi—B5—B2xiii 138.2 (3)Si2i—Na1—Mg1ii 59.53 (4) B5xxi—B5—B2xiii 138.2 (3)Si2ii—Na1—Mg1ii 120.47 (4) B2—B5—B2xiii 38.0 (2)B4viii—Na1—Mg1ii 50.66 (6) Si1—B5—B2xiv 138.2 (3)B4ix—Na1—Mg1ii 129.34 (6) B3xviii—B5—B2xiv 41.2 (4)B4i—Na1—Mg1ii 50.66 (6) B3xxxvi—B5—B2xiv 77.9 (5)B4ii—Na1—Mg1ii 129.34 (6) B3i—B5—B2xiv 111.1 (9)Mg1i—Na1—Mg1ii 180.00 (13) Si1xxi—B5—B2xiv 138.2 (3)B2x—Mg1—B2xi 44.34 (12) B5xxi—B5—B2xiv 138.2 (3)B2x—Mg1—B2xii 46.53 (12) B2—B5—B2xiv 70.5 (5)B2xi—Mg1—B2xii 83.96 (13) B2xiii—B5—B2xiv 39.8 (3)B2x—Mg1—B2xiii 101.12 (17) Si1—B5—B2xi 138.2 (3)B2xi—Mg1—B2xiii 83.96 (13) B3xviii—B5—B2xi 111.0 (9)B2xii—Mg1—B2xiii 83.96 (13) B3xxxvi—B5—B2xi 77.9 (5)B2x—Mg1—B2xiv 83.96 (13) B3i—B5—B2xi 41.2 (4)B2xi—Mg1—B2xiv 101.12 (17) Si1xxi—B5—B2xi 138.2 (3)B2xii—Mg1—B2xiv 44.34 (12) B5xxi—B5—B2xi 138.2 (3)B2xiii—Mg1—B2xiv 46.53 (12) B2—B5—B2xi 39.8 (3)B2x—Mg1—B2 83.96 (13) B2xiii—B5—B2xi 70.5 (5)B2xi—Mg1—B2 46.52 (12) B2xiv—B5—B2xi 83.5 (6)B2xii—Mg1—B2 101.12 (17) Si1—B5—B2xii 138.2 (3)B2xiii—Mg1—B2 44.34 (12) B3xviii—B5—B2xii 77.9 (5)B2xiv—Mg1—B2 83.96 (13) B3xxxvi—B5—B2xii 41.2 (4)B2x—Mg1—Si3 129.43 (9) B3i—B5—B2xii 111.1 (9)B2xi—Mg1—Si3 129.43 (9) Si1xxi—B5—B2xii 138.2 (3)B2xii—Mg1—Si3 129.43 (9) B5xxi—B5—B2xii 138.2 (3)B2xiii—Mg1—Si3 129.43 (9) B2—B5—B2xii 83.5 (6)B2xiv—Mg1—Si3 129.43 (9) B2xiii—B5—B2xii 70.5 (5)B2—Mg1—Si3 129.43 (9) B2xiv—B5—B2xii 38.0 (2)B2x—Mg1—B4xv 85.59 (9) B2xi—B5—B2xii 70.5 (5)B2xi—Mg1—B4xv 43.37 (9) Si1—B5—B2x 138.2 (3)B2xii—Mg1—B4xv 127.11 (15) B3xviii—B5—B2x 111.1 (9)B2xiii—Mg1—B4xv 85.59 (9) B3xxxvi—B5—B2x 41.2 (4)B2xiv—Mg1—B4xv 127.11 (15) B3i—B5—B2x 77.9 (5)B2—Mg1—B4xv 43.37 (9) Si1xxi—B5—B2x 138.2 (3)Si3—Mg1—B4xv 96.04 (11) B5xxi—B5—B2x 138.2 (3)B2x—Mg1—B4xvi 43.37 (9) B2—B5—B2x 70.5 (5)B2xi—Mg1—B4xvi 85.59 (9) B2xiii—B5—B2x 83.5 (6)B2xii—Mg1—B4xvi 43.37 (9) B2xiv—B5—B2x 70.5 (5)B2xiii—Mg1—B4xvi 127.11 (15) B2xi—B5—B2x 38.0 (2)B2xiv—Mg1—B4xvi 85.59 (9) B2xii—B5—B2x 39.8 (3)B2—Mg1—B4xvi 127.11 (15) B5—Si1—Si1xxi 180.0Si3—Mg1—B4xvi 96.04 (11) B5—Si1—B3xviii 59.53 (17)B4xv—Mg1—B4xvi 118.91 (4) Si1xxi—Si1—B3xviii 120.47 (17)B2x—Mg1—B4xvii 127.11 (15) B5—Si1—B3xxxvi 59.53 (17)B2xi—Mg1—B4xvii 127.11 (15) Si1xxi—Si1—B3xxxvi 120.47 (17)B2xii—Mg1—B4xvii 85.59 (9) B3xviii—Si1—B3xxxvi 96.6 (2)supporting informationsup-8Acta Cryst. (2022). E78, 203-206    B2xiii—Mg1—B4xvii 43.37 (9) B5—Si1—B3i 59.53 (17)B2xiv—Mg1—B4xvii 43.37 (9) Si1xxi—Si1—B3i 120.47 (17)B2—Mg1—B4xvii 85.59 (9) B3xviii—Si1—B3i 96.6 (2)Si3—Mg1—B4xvii 96.04 (11) B3xxxvi—Si1—B3i 96.6 (2)B4xv—Mg1—B4xvii 118.91 (4) B5—Si1—B5xxi 180.0B4xvi—Mg1—B4xvii 118.91 (4) Si1xxi—Si1—B5xxi 0.0B2x—Mg1—Si2xv 112.42 (6) B3xviii—Si1—B5xxi 120.47 (17)B2xi—Mg1—Si2xv 82.24 (6) B3xxxvi—Si1—B5xxi 120.47 (17)B2xii—Mg1—Si2xv 157.19 (6) B3i—Si1—B5xxi 120.47 (17)B2xiii—Mg1—Si2xv 112.42 (6) B5—Si1—Na1xiv 98.18 (5)B2xiv—Mg1—Si2xv 157.19 (6) Si1xxi—Si1—Na1xiv 81.82 (5)B2—Mg1—Si2xv 82.24 (6) B3xviii—Si1—Na1xiv 144.19 (12)Si3—Mg1—Si2xv 52.19 (6) B3xxxvi—Si1—Na1xiv 48.18 (10)B4xv—Mg1—Si2xv 43.85 (8) B3i—Si1—Na1xiv 94.136 (18)B4xvi—Mg1—Si2xv 117.22 (8) B5xxi—Si1—Na1xiv 81.82 (5)B4xvii—Mg1—Si2xv 117.22 (8) B5—Si1—Na1xxii 98.18 (5)B2x—Mg1—Si2xvii 157.19 (6) Si1xxi—Si1—Na1xxii 81.82 (5)B2xi—Mg1—Si2xvii 157.19 (6) B3xviii—Si1—Na1xxii 48.18 (10)B2xii—Mg1—Si2xvii 112.42 (6) B3xxxvi—Si1—Na1xxii 144.19 (12)B2xiii—Mg1—Si2xvii 82.24 (6) B3i—Si1—Na1xxii 94.136 (18)B2xiv—Mg1—Si2xvii 82.24 (6) B5xxi—Si1—Na1xxii 81.82 (5)B2—Mg1—Si2xvii 112.42 (6) Na1xiv—Si1—Na1xxii 163.65 (11)Si3—Mg1—Si2xvii 52.19 (6) B5—Si1—Na1xxxvii 98.18 (5)B4xv—Mg1—Si2xvii 117.22 (8) Si1xxi—Si1—Na1xxxvii 81.82 (5)B4xvi—Mg1—Si2xvii 117.21 (8) B3xviii—Si1—Na1xxxvii 144.19 (12)B4xvii—Mg1—Si2xvii 43.85 (8) B3xxxvi—Si1—Na1xxxvii 94.135 (18)Si2xv—Mg1—Si2xvii 86.35 (8) B3i—Si1—Na1xxxvii 48.18 (10)B3xviii—B1—B2iv 108.06 (16) B5xxi—Si1—Na1xxxvii 81.82 (5)B3xviii—B1—B1xix 107.43 (15) Na1xiv—Si1—Na1xxxvii 59.328 (9)B2iv—B1—B1xix 60.40 (13) Na1xxii—Si1—Na1xxxvii 118.01 (3)B3xviii—B1—B2xiv 60.52 (15) B5—Si1—Na1xxxviii 98.18 (5)B2iv—B1—B2xiv 108.83 (15) Si1xxi—Si1—Na1xxxviii 81.82 (5)B1xix—B1—B2xiv 59.60 (13) B3xviii—Si1—Na1xxxviii 94.137 (18)B3xviii—B1—B4ix 59.85 (16) B3xxxvi—Si1—Na1xxxviii 48.19 (10)B2iv—B1—B4ix 60.63 (15) B3i—Si1—Na1xxxviii 144.19 (12)B1xix—B1—B4ix 108.74 (15) B5xxi—Si1—Na1xxxviii 81.82 (5)B2xiv—B1—B4ix 109.26 (16) Na1xiv—Si1—Na1xxxviii 59.328 (9)B3xviii—B1—Si2i 110.42 (15) Na1xxii—Si1—Na1xxxviii 118.01 (3)B2iv—B1—Si2i 136.22 (14) Na1xxxvii—Si1—Na1xxxviii 118.01 (3)B1xix—B1—Si2i 123.70 (8) B5—Si1—Na1 98.18 (5)B2xiv—B1—Si2i 107.77 (13) Si1xxi—Si1—Na1 81.82 (5)B4ix—B1—Si2i 125.94 (15) B3xviii—Si1—Na1 48.19 (10)B3xviii—B1—Na1 125.76 (15) B3xxxvi—Si1—Na1 94.137 (18)B2iv—B1—Na1 70.74 (10) B3i—Si1—Na1 144.19 (12)B1xix—B1—Na1 116.13 (15) B5xxi—Si1—Na1 81.82 (5)B2xiv—B1—Na1 173.69 (13) Na1xiv—Si1—Na1 118.01 (3)B4ix—B1—Na1 76.20 (11) Na1xxii—Si1—Na1 59.328 (9)Si2i—B1—Na1 70.23 (6) Na1xxxvii—Si1—Na1 163.65 (11)supporting informationsup-9Acta Cryst. (2022). E78, 203-206    B3xviii—B1—B5 26.44 (12) Na1xxxviii—Si1—Na1 59.329 (9)B2iv—B1—B5 134.42 (13) B5—Si1—Na1x 98.18 (5)B1xix—B1—B5 118.8 (4) Si1xxi—Si1—Na1x 81.82 (5)B2xiv—B1—B5 60.4 (4) B3xviii—Si1—Na1x 94.135 (18)B4ix—B1—B5 80.5 (2) B3xxxvi—Si1—Na1x 144.19 (12)Si2i—B1—B5 85.06 (18) B3i—Si1—Na1x 48.18 (10)Na1—B1—B5 124.6 (4) B5xxi—Si1—Na1x 81.82 (5)B3xviii—B1—Na1xx 99.62 (14) Na1xiv—Si1—Na1x 118.01 (3)B2iv—B1—Na1xx 99.93 (10) Na1xxii—Si1—Na1x 59.328 (9)B1xix—B1—Na1xx 39.67 (11) Na1xxxvii—Si1—Na1x 59.328 (9)B2xiv—B1—Na1xx 39.15 (8) Na1xxxviii—Si1—Na1x 163.65 (11)B4ix—B1—Na1xx 139.11 (13) Na1—Si1—Na1x 118.01 (3)Si2i—B1—Na1xx 93.52 (7) B1i—Si2—B1xxix 99.44 (13)Na1—B1—Na1xx 134.55 (7) B1i—Si2—B4 112.65 (8)B5—B1—Na1xx 94.3 (3) B1xxix—Si2—B4 112.65 (8)B3xviii—B1—B5i 102.63 (12) B1i—Si2—Si3xv 110.23 (7)B2iv—B1—B5i 23.0 (2) B1xxix—Si2—Si3xv 110.23 (7)B1xix—B1—B5i 39.4 (2) B4—Si2—Si3xv 111.12 (10)B2xiv—B1—B5i 86.6 (2) B1i—Si2—Na1xxxiii 166.61 (7)B4ix—B1—B5i 72.9 (2) B1xxix—Si2—Na1xxxiii 67.56 (6)Si2i—B1—B5i 146.89 (9) B4—Si2—Na1xxxiii 71.60 (4)Na1—B1—B5i 92.17 (19) Si3xv—Si2—Na1xxxiii 78.52 (2)B5—B1—B5i 127.32 (17) B1i—Si2—Na1xxiv 67.56 (6)Na1xx—B1—B5i 78.9 (2) B1xxix—Si2—Na1xxiv 166.61 (7)B3xviii—B1—B5xxi 45.13 (19) B4—Si2—Na1xxiv 71.60 (4)B2iv—B1—B5xxi 127.76 (14) Si3xv—Si2—Na1xxiv 78.52 (2)B1xix—B1—B5xxi 151.4 (2) Na1xxxiii—Si2—Na1xxiv 125.18 (3)B2xiv—B1—B5xxi 93.9 (2) B1i—Si2—Mg1xv 130.08 (7)B4ix—B1—B5xxi 67.63 (14) B1xxix—Si2—Mg1xv 130.08 (6)Si2i—B1—B5xxi 71.88 (9) B4—Si2—Mg1xv 58.69 (11)Na1—B1—B5xxi 91.1 (2) Si3xv—Si2—Mg1xv 52.42 (7)B5—B1—B5xxi 33.5 (6) Na1xxxiii—Si2—Mg1xv 63.235 (15)Na1xx—B1—B5xxi 124.81 (18) Na1xxiv—Si2—Mg1xv 63.235 (15)B5i—B1—B5xxi 138.30 (13) B1i—Si2—B5i 60.03 (17)B3xviii—B1—Na1xxii 58.43 (12) B1xxix—Si2—B5i 60.03 (17)B2iv—B1—Na1xxii 59.13 (9) B4—Si2—B5i 87.2 (3)B1xix—B1—Na1xxii 105.05 (8) Si3xv—Si2—B5i 161.7 (3)B2xiv—B1—Na1xxii 105.67 (11) Na1xxxiii—Si2—B5i 108.61 (12)B4ix—B1—Na1xxii 4.27 (10) Na1xxiv—Si2—B5i 108.61 (12)Si2i—B1—Na1xxii 130.03 (8) Mg1xv—Si2—B5i 145.8 (3)Na1—B1—Na1xxii 79.66 (5) B1i—Si2—B5xxx 80.55 (17)B5—B1—Na1xxii 80.33 (15) B1xxix—Si2—B5xxx 80.55 (17)Na1xx—B1—Na1xxii 134.85 (5) B4—Si2—B5xxx 51.3 (3)B5i—B1—Na1xxii 70.00 (18) Si3xv—Si2—B5xxx 162.4 (2)B5xxi—B1—Na1xxii 69.77 (5) Na1xxxiii—Si2—B5xxx 93.66 (11)B2xiii—B2—B1xxiii 131.14 (10) Na1xxiv—Si2—B5xxx 93.66 (11)B2xiii—B2—B1x 111.97 (10) Mg1xv—Si2—B5xxx 110.0 (2)B1xxiii—B2—B1x 60.00 (14) B5i—Si2—B5xxx 35.9 (6)supporting informationsup-10Acta Cryst. (2022). E78, 203-206    B2xiii—B2—B3i 106.92 (13) B1i—Si2—Na1xxii 59.92 (6)B1xxiii—B2—B3i 106.68 (18) B1xxix—Si2—Na1xxii 59.92 (6)B1x—B2—B3i 59.15 (14) B4—Si2—Na1xxii 165.73 (10)B2xiii—B2—B4xv 136.84 (12) Si3xv—Si2—Na1xxii 83.15 (4)B1xxiii—B2—B4xv 60.14 (13) Na1xxxiii—Si2—Na1xxii 112.858 (15)B1x—B2—B4xv 108.04 (17) Na1xxiv—Si2—Na1xxii 112.858 (15)B3i—B2—B4xv 106.97 (16) Mg1xv—Si2—Na1xxii 135.57 (6)B2xiii—B2—B2xi 120.000 (1) B5i—Si2—Na1xxii 78.6 (3)B1xxiii—B2—B2xi 107.39 (10) B5xxx—Si2—Na1xxii 114.5 (2)B1x—B2—B2xi 107.25 (10) B1i—Si2—Na1xxxix 123.16 (7)B3i—B2—B2xi 59.51 (9) B1xxix—Si2—Na1xxxix 123.16 (7)B4xv—B2—B2xi 59.65 (9) B4—Si2—Na1xxxix 85.66 (9)B2xiii—B2—Mg1 67.83 (6) Si3xv—Si2—Na1xxxix 25.46 (4)B1xxiii—B2—Mg1 127.40 (14) Na1xxxiii—Si2—Na1xxxix 69.017 (15)B1x—B2—Mg1 171.03 (15) Na1xxiv—Si2—Na1xxxix 69.017 (15)B3i—B2—Mg1 112.01 (15) Mg1xv—Si2—Na1xxxix 26.96 (6)B4xv—B2—Mg1 75.16 (13) B5i—Si2—Na1xxxix 172.8 (3)B2xi—B2—Mg1 66.74 (6) B5xxx—Si2—Na1xxxix 136.9 (2)B2xiii—B2—B5 71.01 (12) Na1xxii—Si2—Na1xxxix 108.610 (15)B1xxiii—B2—B5 142.0 (3) Si3xl—Si3—Si2xv 104.62 (4)B1x—B2—B5 83.9 (3) Si3xl—Si3—Si2xvi 104.61 (4)B3i—B2—B5 37.8 (2) Si2xv—Si3—Si2xvi 113.86 (3)B4xv—B2—B5 129.70 (16) Si3xl—Si3—Si2xvii 104.61 (4)B2xi—B2—B5 70.08 (13) Si2xv—Si3—Si2xvii 113.86 (3)Mg1—B2—B5 87.7 (3) Si2xvi—Si3—Si2xvii 113.86 (3)B2xiii—B2—Na1xxiv 71.62 (5) Si3xl—Si3—Mg1 180.0B1xxiii—B2—Na1xxiv 71.82 (10) Si2xv—Si3—Mg1 75.38 (4)B1x—B2—Na1xxiv 116.66 (12) Si2xvi—Si3—Mg1 75.39 (4)B3i—B2—Na1xxiv 175.02 (13) Si2xvii—Si3—Mg1 75.39 (4)B4xv—B2—Na1xxiv 76.58 (10) Si3xl—Si3—Na1xx 118.76 (3)B2xi—B2—Na1xxiv 125.43 (5) Si2xv—Si3—Na1xx 136.62 (7)Mg1—B2—Na1xxiv 72.08 (8) Si2xvi—Si3—Na1xx 56.938 (18)B5—B2—Na1xxiv 142.00 (18) Si2xvii—Si3—Na1xx 56.938 (18)B2xiii—B2—Na1xxv 113.62 (3) Mg1—Si3—Na1xx 61.24 (3)B1xxiii—B2—Na1xxv 98.99 (11) Si3xl—Si3—Na1xxv 118.76 (3)B1x—B2—Na1xxv 131.77 (12) Si2xv—Si3—Na1xxv 56.938 (18)B3i—B2—Na1xxv 92.82 (10) Si2xvi—Si3—Na1xxv 56.940 (18)B4xv—B2—Na1xxv 39.10 (9) Si2xvii—Si3—Na1xxv 136.62 (7)B2xi—B2—Na1xxv 33.32 (3) Mg1—Si3—Na1xxv 61.24 (3)Mg1—B2—Na1xxv 46.23 (4) Na1xx—Si3—Na1xxv 98.79 (3)B5—B2—Na1xxv 96.5 (2) Si3xl—Si3—Na1xxiv 118.76 (3)Na1xxiv—B2—Na1xxv 92.11 (5) Si2xv—Si3—Na1xxiv 56.938 (18)B2xiii—B2—B5xxvi 157.80 (15) Si2xvi—Si3—Na1xxiv 136.62 (7)B1xxiii—B2—B5xxvi 29.13 (9) Si2xvii—Si3—Na1xxiv 56.940 (18)B1x—B2—B5xxvi 69.9 (2) Mg1—Si3—Na1xxiv 61.24 (3)B3i—B2—B5xxvi 93.1 (3) Na1xx—Si3—Na1xxiv 98.79 (3)B4xv—B2—B5xxvi 38.8 (2) Na1xxv—Si3—Na1xxiv 98.78 (3)B2xi—B2—B5xxvi 78.28 (3) Si3xl—Si3—Na1xli 36.851 (12)supporting informationsup-11Acta Cryst. (2022). E78, 203-206    Mg1—B2—B5xxvi 113.9 (2) Si2xv—Si3—Na1xli 67.76 (3)B5—B2—B5xxvi 130.32 (9) Si2xvi—Si3—Na1xli 119.48 (4)Na1xxiv—B2—B5xxvi 87.6 (2) Si2xvii—Si3—Na1xli 119.48 (4)Na1xxv—B2—B5xxvi 73.92 (14) Mg1—Si3—Na1xli 143.149 (12)B2xiii—B2—Na1x 111.07 (3) Na1xx—Si3—Na1xli 155.61 (4)B1xxiii—B2—Na1x 57.51 (9) Na1xxv—Si3—Na1xli 97.015 (14)B1x—B2—Na1x 3.84 (8) Na1xxiv—Si3—Na1xli 97.015 (14)B3i—B2—Na1x 62.97 (11) Si3xl—Si3—Na1xlii 36.852 (12)B4xv—B2—Na1x 107.75 (13) Si2xv—Si3—Na1xlii 119.48 (4)B2xi—B2—Na1x 110.53 (3) Si2xvi—Si3—Na1xlii 119.48 (4)Mg1—B2—Na1x 174.62 (10) Si2xvii—Si3—Na1xlii 67.76 (3)B5—B2—Na1x 87.0 (3) Mg1—Si3—Na1xlii 143.148 (12)Na1xxiv—B2—Na1x 112.83 (6) Na1xx—Si3—Na1xlii 97.015 (14)Na1xxv—B2—Na1x 133.76 (6) Na1xxv—Si3—Na1xlii 155.61 (4)B5xxvi—B2—Na1x 69.2 (2) Na1xxiv—Si3—Na1xlii 97.016 (14)B5i—B3—B1xxvii 125.38 (12) Na1xli—Si3—Na1xlii 62.58 (2)B5i—B3—B1iv 125.38 (12) Si3xl—Si3—Na1xliii 36.852 (12)B1xxvii—B3—B1iv 109.1 (2) Si2xv—Si3—Na1xliii 119.48 (4)B5i—B3—B4xxviii 144.1 (7) Si2xvi—Si3—Na1xliii 67.76 (3)B1xxvii—B3—B4xxviii 60.74 (14) Si2xvii—Si3—Na1xliii 119.48 (4)B1iv—B3—B4xxviii 60.74 (14) Mg1—Si3—Na1xliii 143.148 (12)B5i—B3—B2i 101.0 (6) Na1xx—Si3—Na1xliii 97.015 (14)B1xxvii—B3—B2i 60.33 (12) Na1xxv—Si3—Na1xliii 97.016 (14)B1iv—B3—B2i 109.4 (2) Na1xxiv—Si3—Na1xliii 155.61 (4)B4xxviii—B3—B2i 109.8 (2) Na1xli—Si3—Na1xliii 62.58 (2)B5i—B3—B2xxix 101.0 (6) Na1xlii—Si3—Na1xliii 62.58 (2)B1xxvii—B3—B2xxix 109.4 (2)Symmetry codes: (i) −x+2/3, −y+1/3, −z+1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) −x+y+1/3, y−1/3, z−1/3; (iv) x−y+2/3, −y+1/3, −z+1/3; (v) −x+1, −y, −z; (vi) −x+y+1, y, z; (vii) x−y, −y, −z; (viii) x−y+2/3, x−2/3, −z+1/3; (ix) −x+y+1/3, −x+2/3, z−1/3; (x) −y, x−y, z; (xi) −y, −x, z; (xii) x, x−y, z; (xiii) −x+y, y, z; (xiv) −x+y, −x, z; (xv) −x+1/3, −y+2/3, −z+2/3; (xvi) y−2/3, −x+y−1/3, −z+2/3; (xvii) x−y+1/3, x−1/3, −z+2/3; (xviii) x−y−1/3, x−2/3, −z+1/3; (xix) −x+2/3, −x+y+1/3, −z+1/3; (xx) −x+y+2/3, −x+1/3, z+1/3; (xxi) −x, −y, −z; (xxii) −x+y+1, −x+1, z; (xxiii) x−y−1/3, −y+1/3, −z+1/3; (xxiv) x−1/3, y+1/3, z+1/3; (xxv) −y−1/3, x−y−2/3, z+1/3; (xxvi) −x−1/3, −y+1/3, −z+1/3; (xxvii) y+2/3, −x+y+1/3, −z+1/3; (xxviii) −x+4/3, −y+2/3, −z+2/3; (xxix) y+2/3, x+1/3, −z+1/3; (xxx) x+2/3, y+1/3, z+1/3; (xxxi) −y+2/3, x−y−2/3, z+1/3; (xxxii) −y+1, x−y, z; (xxxiii) −y+2/3, x−y+1/3, z+1/3; (xxxiv) −x+y+2/3, y+1/3, z+1/3; (xxxv) y+1/3, x+2/3, −z+2/3; (xxxvi) y−1/3, −x+y+1/3, −z+1/3; (xxxvii) x−1, y, z; (xxxviii) −y, x−y−1, z; (xxxix) −x+y+2/3, −x+4/3, z+1/3; (xl) −x, −y, −z+1; (xli) −x+y+1/3, −x+2/3, z+2/3; (xlii) −y+1/3, x−y−1/3, z+2/3; (xliii) x−2/3, y−1/3, z+2/3.