The crystal structure described by MgV12(BO5)4 crystallizes in the monoclinic Pm space group. Mg(1) is bonded in a 5-coordinate geometry to one O(19), two equivalent O(1), and two equivalent O(5) atoms. There are twelve inequivalent V sites. In the first V site, V(1) is bonded to one O(20), one O(9), two equivalent O(16), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 58-68°. In the second V site, V(2) is bonded to one O(10), one O(19), two equivalent O(15), and two equivalent O(6) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 63-65°. In the third V site, V(3) is bonded to one O(11), one O(18), two equivalent O(14), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 65°. In the fourth V site, V(4) is bonded to one O(12), one O(17), two equivalent O(13), and two equivalent O(8) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 53-69°. In the fifth V site, V(5) is bonded to one O(10), one O(9), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 65-68°. In the sixth V site, V(6) is bonded to one O(11), one O(12), two equivalent O(1), and two equivalent O(2) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the seventh V site, V(7) is bonded to one O(13), one O(3), two equivalent O(17), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 19-58°. In the eighth V site, V(8) is bonded to one O(14), one O(4), two equivalent O(10), and two equivalent O(18) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 19-63°. In the ninth V site, V(9) is bonded in a 5-coordinate geometry to one O(15), two equivalent O(11), and two equivalent O(19) atoms. In the tenth V site, V(10) is bonded to one O(16), one O(2), two equivalent O(12), and two equivalent O(20) atoms to form a mixture of distorted corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 69°. In the eleventh V site, V(11) is bonded in a 5-coordinate geometry to one O(6), two equivalent O(19), and two equivalent O(20) atoms. In the twelfth V site, V(12) is bonded to one O(7), one O(8), two equivalent O(17), and two equivalent O(18) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 19°. There are four inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(1), one O(13), and one O(5) atom. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(14), one O(2), and one O(6) atom. In the third B site, B(3) is bonded in a trigonal planar geometry to one O(15), one O(3), and one O(7) atom. In the fourth B site, B(4) is bonded in a trigonal planar geometry to one O(16), one O(4), and one O(8) atom. There are twenty inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent Mg(1), two equivalent V(6), and one B(1) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one V(10), two equivalent V(6), and one B(2) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one V(7), two equivalent V(5), and one B(3) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(8), two equivalent V(5), and one B(4) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to two equivalent Mg(1), two equivalent V(1), and one B(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one V(11), two equivalent V(2), and one B(2) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one V(12), two equivalent V(3), and one B(3) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one V(12), two equivalent V(4), and one B(4) atom. In the ninth O site, O(9) is bonded to one V(1), one V(5), and two equivalent V(7) atoms to form OV4 tetrahedra that share corners with two equivalent O(17)V5 square pyramids,  a cornercorner with one O(10)V4 tetrahedra, corners with two equivalent O(9)V4 tetrahedra,  a cornercorner with one O(20)V5 trigonal bipyramid, and  an edgeedge with one O(17)V5 square pyramid. In the tenth O site, O(10) is bonded to one V(2), one V(5), and two equivalent V(8) atoms to form OV4 tetrahedra that share  a cornercorner with one O(19)MgV5 octahedra, corners with two equivalent O(18)V5 square pyramids,  a cornercorner with one O(9)V4 tetrahedra, corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(10)V4 tetrahedra, and  an edgeedge with one O(18)V5 square pyramid. The corner-sharing octahedral tilt angles are 1°. In the eleventh O site, O(11) is bonded to one V(3), one V(6), and two equivalent V(9) atoms to form distorted OV4 tetrahedra that share corners with two equivalent O(19)MgV5 octahedra,  a cornercorner with one O(18)V5 square pyramid,  a cornercorner with one O(12)V4 tetrahedra, corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(11)V4 tetrahedra, and  an edgeedge with one O(19)MgV5 octahedra. The corner-sharing octahedral tilt angles are 24°. In the twelfth O site, O(12) is bonded to one V(4), one V(6), and two equivalent V(10) atoms to form OV4 tetrahedra that share  a cornercorner with one O(17)V5 square pyramid,  a cornercorner with one O(11)V4 tetrahedra, corners with two equivalent O(12)V4 tetrahedra, corners with two equivalent O(20)V5 trigonal bipyramids, and  an edgeedge with one O(20)V5 trigonal bipyramid. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one V(7), two equivalent V(4), and one B(1) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one V(8), two equivalent V(3), and one B(2) atom. In the fifteenth O site, O(15) is bonded to one V(9), two equivalent V(2), and one B(3) atom to form distorted OV3B tetrahedra that share corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(10)V4 tetrahedra, corners with two equivalent O(11)V4 tetrahedra, and edges with two equivalent O(19)MgV5 octahedra. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one V(10), two equivalent V(1), and one B(4) atom. In the seventeenth O site, O(17) is bonded to one V(4), two equivalent V(12), and two equivalent V(7) atoms to form OV5 square pyramids that share corners with two equivalent O(18)V5 square pyramids,  a cornercorner with one O(12)V4 tetrahedra, corners with two equivalent O(9)V4 tetrahedra,  an edgeedge with one O(18)V5 square pyramid, edges with two equivalent O(17)V5 square pyramids, and  an edgeedge with one O(9)V4 tetrahedra. In the eighteenth O site, O(18) is bonded to one V(3), two equivalent V(12), and two equivalent V(8) atoms to form OV5 square pyramids that share corners with two equivalent O(17)V5 square pyramids,  a cornercorner with one O(11)V4 tetrahedra, corners with two equivalent O(10)V4 tetrahedra,  an edgeedge with one O(17)V5 square pyramid, edges with two equivalent O(18)V5 square pyramids, and  an edgeedge with one O(10)V4 tetrahedra. In the nineteenth O site, O(19) is bonded to one Mg(1), one V(2), two equivalent V(11), and two equivalent V(9) atoms to form OMgV5 octahedra that share  a cornercorner with one O(10)V4 tetrahedra, corners with two equivalent O(11)V4 tetrahedra, corners with two equivalent O(20)V5 trigonal bipyramids, edges with two equivalent O(19)MgV5 octahedra,  an edgeedge with one O(11)V4 tetrahedra, edges with two equivalent O(15)V3B tetrahedra, and  an edgeedge with one O(20)V5 trigonal bipyramid. In the twentieth O site, O(20) is bonded to one V(1), two equivalent V(10), and two equivalent V(11) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(19)MgV5 octahedra,  a cornercorner with one O(9)V4 tetrahedra, corners with two equivalent O(12)V4 tetrahedra,  an edgeedge with one O(19)MgV5 octahedra,  an edgeedge with one O(12)V4 tetrahedra, and edges with two equivalent O(20)V5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 18°. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgV12(BO5)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.162
_cell_length_b   9.693
_cell_length_c   13.017
_cell_angle_alpha   88.679
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   398.859
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Mg  Mg0  1  0.500  0.210  0.035  1.0
  V  V1  1  0.500  0.003  0.230  1.0
  V  V2  1  0.500  0.983  0.768  1.0
  V  V3  1  0.500  0.491  0.722  1.0
  V  V4  1  0.500  0.520  0.288  1.0
  V  V5  1  0.500  1.000  0.498  1.0
  V  V6  1  0.500  0.515  0.999  1.0
  V  V7  1  0.000  0.251  0.394  1.0
  V  V8  1  1.000  0.749  0.609  1.0
  V  V9  1  0.000  0.253  0.857  1.0
  V  V10  1  1.000  0.743  0.123  1.0
  V  V11  1  0.000  0.965  0.987  1.0
  V  V12  1  0.000  0.499  0.504  1.0
  B  B13  1  0.000  0.298  0.161  1.0
  B  B14  1  1.000  0.716  0.853  1.0
  B  B15  1  0.000  0.217  0.635  1.0
  B  B16  1  0.000  0.780  0.364  1.0
  O  O17  1  1.000  0.359  0.061  1.0
  O  O18  1  1.000  0.654  0.951  1.0
  O  O19  1  0.000  0.152  0.542  1.0
  O  O20  1  0.000  0.849  0.456  1.0
  O  O21  1  0.000  0.152  0.150  1.0
  O  O22  1  0.000  0.860  0.847  1.0
  O  O23  1  0.000  0.361  0.643  1.0
  O  O24  1  0.000  0.636  0.363  1.0
  O  O25  1  0.500  0.121  0.361  1.0
  O  O26  1  0.500  0.877  0.634  1.0
  O  O27  1  0.500  0.385  0.868  1.0
  O  O28  1  0.500  0.616  0.141  1.0
  O  O29  1  0.000  0.367  0.249  1.0
  O  O30  1  1.000  0.642  0.763  1.0
  O  O31  1  0.000  0.135  0.726  1.0
  O  O32  1  0.000  0.853  0.269  1.0
  O  O33  1  0.500  0.398  0.427  1.0
  O  O34  1  0.500  0.603  0.579  1.0
  O  O35  1  0.500  0.095  0.916  1.0
  O  O36  1  0.500  0.896  0.082  1.0
[/CIF]
.
The crystal structure described by MgV12(BO5)4 crystallizes in the monoclinic Pm space group. Mg(1) is bonded in a 5-coordinate geometry to one O(19), two equivalent O(1), and two equivalent O(5) atoms. There are twelve inequivalent V sites. In the first V site, V(1) is bonded to one O(20), one O(9), two equivalent O(16), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 58-68°. In the second V site, V(2) is bonded to one O(10), one O(19), two equivalent O(15), and two equivalent O(6) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 63-65°. In the third V site, V(3) is bonded to one O(11), one O(18), two equivalent O(14), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 65°. In the fourth V site, V(4) is bonded to one O(12), one O(17), two equivalent O(13), and two equivalent O(8) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 53-69°. In the fifth V site, V(5) is bonded to one O(10), one O(9), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 65-68°. In the sixth V site, V(6) is bonded to one O(11), one O(12), two equivalent O(1), and two equivalent O(2) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the seventh V site, V(7) is bonded to one O(13), one O(3), two equivalent O(17), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 19-58°. In the eighth V site, V(8) is bonded to one O(14), one O(4), two equivalent O(10), and two equivalent O(18) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 19-63°. In the ninth V site, V(9) is bonded in a 5-coordinate geometry to one O(15), two equivalent O(11), and two equivalent O(19) atoms. In the tenth V site, V(10) is bonded to one O(16), one O(2), two equivalent O(12), and two equivalent O(20) atoms to form a mixture of distorted corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 69°. In the eleventh V site, V(11) is bonded in a 5-coordinate geometry to one O(6), two equivalent O(19), and two equivalent O(20) atoms. In the twelfth V site, V(12) is bonded to one O(7), one O(8), two equivalent O(17), and two equivalent O(18) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 19°. There are four inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(1), one O(13), and one O(5) atom. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(14), one O(2), and one O(6) atom. In the third B site, B(3) is bonded in a trigonal planar geometry to one O(15), one O(3), and one O(7) atom. In the fourth B site, B(4) is bonded in a trigonal planar geometry to one O(16), one O(4), and one O(8) atom. There are twenty inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent Mg(1), two equivalent V(6), and one B(1) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one V(10), two equivalent V(6), and one B(2) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one V(7), two equivalent V(5), and one B(3) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(8), two equivalent V(5), and one B(4) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to two equivalent Mg(1), two equivalent V(1), and one B(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one V(11), two equivalent V(2), and one B(2) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one V(12), two equivalent V(3), and one B(3) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one V(12), two equivalent V(4), and one B(4) atom. In the ninth O site, O(9) is bonded to one V(1), one V(5), and two equivalent V(7) atoms to form OV4 tetrahedra that share corners with two equivalent O(17)V5 square pyramids,  a cornercorner with one O(10)V4 tetrahedra, corners with two equivalent O(9)V4 tetrahedra,  a cornercorner with one O(20)V5 trigonal bipyramid, and  an edgeedge with one O(17)V5 square pyramid. In the tenth O site, O(10) is bonded to one V(2), one V(5), and two equivalent V(8) atoms to form OV4 tetrahedra that share  a cornercorner with one O(19)MgV5 octahedra, corners with two equivalent O(18)V5 square pyramids,  a cornercorner with one O(9)V4 tetrahedra, corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(10)V4 tetrahedra, and  an edgeedge with one O(18)V5 square pyramid. The corner-sharing octahedral tilt angles are 1°. In the eleventh O site, O(11) is bonded to one V(3), one V(6), and two equivalent V(9) atoms to form distorted OV4 tetrahedra that share corners with two equivalent O(19)MgV5 octahedra,  a cornercorner with one O(18)V5 square pyramid,  a cornercorner with one O(12)V4 tetrahedra, corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(11)V4 tetrahedra, and  an edgeedge with one O(19)MgV5 octahedra. The corner-sharing octahedral tilt angles are 24°. In the twelfth O site, O(12) is bonded to one V(4), one V(6), and two equivalent V(10) atoms to form OV4 tetrahedra that share  a cornercorner with one O(17)V5 square pyramid,  a cornercorner with one O(11)V4 tetrahedra, corners with two equivalent O(12)V4 tetrahedra, corners with two equivalent O(20)V5 trigonal bipyramids, and  an edgeedge with one O(20)V5 trigonal bipyramid. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one V(7), two equivalent V(4), and one B(1) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one V(8), two equivalent V(3), and one B(2) atom. In the fifteenth O site, O(15) is bonded to one V(9), two equivalent V(2), and one B(3) atom to form distorted OV3B tetrahedra that share corners with two equivalent O(15)V3B tetrahedra, corners with two equivalent O(10)V4 tetrahedra, corners with two equivalent O(11)V4 tetrahedra, and edges with two equivalent O(19)MgV5 octahedra. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one V(10), two equivalent V(1), and one B(4) atom. In the seventeenth O site, O(17) is bonded to one V(4), two equivalent V(12), and two equivalent V(7) atoms to form OV5 square pyramids that share corners with two equivalent O(18)V5 square pyramids,  a cornercorner with one O(12)V4 tetrahedra, corners with two equivalent O(9)V4 tetrahedra,  an edgeedge with one O(18)V5 square pyramid, edges with two equivalent O(17)V5 square pyramids, and  an edgeedge with one O(9)V4 tetrahedra. In the eighteenth O site, O(18) is bonded to one V(3), two equivalent V(12), and two equivalent V(8) atoms to form OV5 square pyramids that share corners with two equivalent O(17)V5 square pyramids,  a cornercorner with one O(11)V4 tetrahedra, corners with two equivalent O(10)V4 tetrahedra,  an edgeedge with one O(17)V5 square pyramid, edges with two equivalent O(18)V5 square pyramids, and  an edgeedge with one O(10)V4 tetrahedra. In the nineteenth O site, O(19) is bonded to one Mg(1), one V(2), two equivalent V(11), and two equivalent V(9) atoms to form OMgV5 octahedra that share  a cornercorner with one O(10)V4 tetrahedra, corners with two equivalent O(11)V4 tetrahedra, corners with two equivalent O(20)V5 trigonal bipyramids, edges with two equivalent O(19)MgV5 octahedra,  an edgeedge with one O(11)V4 tetrahedra, edges with two equivalent O(15)V3B tetrahedra, and  an edgeedge with one O(20)V5 trigonal bipyramid. In the twentieth O site, O(20) is bonded to one V(1), two equivalent V(10), and two equivalent V(11) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(19)MgV5 octahedra,  a cornercorner with one O(9)V4 tetrahedra, corners with two equivalent O(12)V4 tetrahedra,  an edgeedge with one O(19)MgV5 octahedra,  an edgeedge with one O(12)V4 tetrahedra, and edges with two equivalent O(20)V5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 18°. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgV12(BO5)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.162
_cell_length_b   9.693
_cell_length_c   13.017
_cell_angle_alpha   88.679
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   398.859
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Mg  Mg0  1  0.500  0.210  0.035  1.0
  V  V1  1  0.500  0.003  0.230  1.0
  V  V2  1  0.500  0.983  0.768  1.0
  V  V3  1  0.500  0.491  0.722  1.0
  V  V4  1  0.500  0.520  0.288  1.0
  V  V5  1  0.500  1.000  0.498  1.0
  V  V6  1  0.500  0.515  0.999  1.0
  V  V7  1  0.000  0.251  0.394  1.0
  V  V8  1  1.000  0.749  0.609  1.0
  V  V9  1  0.000  0.253  0.857  1.0
  V  V10  1  1.000  0.743  0.123  1.0
  V  V11  1  0.000  0.965  0.987  1.0
  V  V12  1  0.000  0.499  0.504  1.0
  B  B13  1  0.000  0.298  0.161  1.0
  B  B14  1  1.000  0.716  0.853  1.0
  B  B15  1  0.000  0.217  0.635  1.0
  B  B16  1  0.000  0.780  0.364  1.0
  O  O17  1  1.000  0.359  0.061  1.0
  O  O18  1  1.000  0.654  0.951  1.0
  O  O19  1  0.000  0.152  0.542  1.0
  O  O20  1  0.000  0.849  0.456  1.0
  O  O21  1  0.000  0.152  0.150  1.0
  O  O22  1  0.000  0.860  0.847  1.0
  O  O23  1  0.000  0.361  0.643  1.0
  O  O24  1  0.000  0.636  0.363  1.0
  O  O25  1  0.500  0.121  0.361  1.0
  O  O26  1  0.500  0.877  0.634  1.0
  O  O27  1  0.500  0.385  0.868  1.0
  O  O28  1  0.500  0.616  0.141  1.0
  O  O29  1  0.000  0.367  0.249  1.0
  O  O30  1  1.000  0.642  0.763  1.0
  O  O31  1  0.000  0.135  0.726  1.0
  O  O32  1  0.000  0.853  0.269  1.0
  O  O33  1  0.500  0.398  0.427  1.0
  O  O34  1  0.500  0.603  0.579  1.0
  O  O35  1  0.500  0.095  0.916  1.0
  O  O36  1  0.500  0.896  0.082  1.0
[/CIF]
.