The structure described by MgLu6WO12 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 5-coordinate geometry to one O(11), one O(12), one O(2), one O(3), and one O(8) atom. There are six inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), one O(5), and one O(6) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one W(1)O6 octahedra and  an edgeedge with one W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 46°. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(5), one O(6), one O(8), and one O(9) atom. In the fifth Lu site, Lu(5) is bonded in a 6-coordinate geometry to one O(10), one O(12), one O(4), one O(6), one O(7), and one O(8) atom. In the sixth Lu site, Lu(6) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(11), one O(12), one O(3), one O(7), and one O(8) atom. W(1) is bonded to one O(1), one O(11), one O(12), one O(2), one O(4), and one O(9) atom to form WO6 octahedra that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(2), one Lu(6), and one W(1) atom to form OLu3W tetrahedra that share corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), one Lu(1), one Lu(2), one Lu(3), and one Lu(6) atom to form distorted OLu4Mg trigonal bipyramids that share  a cornercorner with one O(1)Lu3W tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra,  a cornercorner with one O(7)Lu4 tetrahedra, corners with two equivalent O(6)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(5)Lu4 tetrahedra,  an edgeedge with one O(7)Lu4 tetrahedra, and  an edgeedge with one O(12)Lu3MgW trigonal bipyramid. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Lu(2), one Lu(3), one Lu(5), and one W(1) atom. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), one Lu(3), and one Lu(4) atom to form OLu4 tetrahedra that share  a cornercorner with one O(6)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the sixth O site, O(6) is bonded to one Lu(1), one Lu(2), one Lu(4), and one Lu(5) atom to form OLu4 tetrahedra that share  a cornercorner with one O(10)Lu4 tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra, corners with two equivalent O(12)Lu3MgW trigonal bipyramids, corners with two equivalent O(3)Lu4Mg trigonal bipyramids,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(5)Lu4 tetrahedra, and  an edgeedge with one O(7)Lu4 tetrahedra. In the seventh O site, O(7) is bonded to one Lu(2), one Lu(3), one Lu(5), and one Lu(6) atom to form OLu4 tetrahedra that share corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Mg(1), one Lu(3), one Lu(4), one Lu(5), and one Lu(6) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Lu(2), one Lu(4), and one W(1) atom. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(4), one Lu(5), and one Lu(6) atom to form distorted OLu4 tetrahedra that share  a cornercorner with one O(6)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(4), one Lu(6), and one W(1) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Lu(1), one Lu(5), one Lu(6), and one W(1) atom to form distorted OLu3MgW trigonal bipyramids that share  a cornercorner with one O(1)Lu3W tetrahedra,  a cornercorner with one O(10)Lu4 tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra, corners with two equivalent O(6)Lu4 tetrahedra,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(7)Lu4 tetrahedra, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu6MgWO12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.538
_cell_length_b   6.299
_cell_length_c   6.546
_cell_angle_alpha   97.769
_cell_angle_beta   100.393
_cell_angle_gamma   98.999
_symmetry_Int_Tables_number   1
_cell_volume   258.165
_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
  Lu  Lu0  1  0.126  0.306  0.635  1.0
  Lu  Lu1  1  0.396  0.862  0.691  1.0
  Lu  Lu2  1  0.346  0.609  0.149  1.0
  Lu  Lu3  1  0.655  0.396  0.825  1.0
  Lu  Lu4  1  0.575  0.139  0.325  1.0
  Lu  Lu5  1  0.870  0.739  0.414  1.0
  Mg  Mg6  1  0.938  0.369  0.193  1.0
  W  W7  1  0.999  0.974  0.992  1.0
  O  O8  1  0.071  0.938  0.689  1.0
  O  O9  1  0.109  0.305  0.979  1.0
  O  O10  1  0.164  0.570  0.410  1.0
  O  O11  1  0.315  0.939  0.080  1.0
  O  O12  1  0.397  0.568  0.822  1.0
  O  O13  1  0.409  0.184  0.575  1.0
  O  O14  1  0.567  0.816  0.427  1.0
  O  O15  1  0.621  0.423  0.172  1.0
  O  O16  1  0.705  0.057  0.890  1.0
  O  O17  1  0.822  0.427  0.578  1.0
  O  O18  1  0.913  0.671  0.057  1.0
  O  O19  1  0.921  0.084  0.306  1.0
[/CIF]
.
The structure described by MgLu6WO12 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 5-coordinate geometry to one O(11), one O(12), one O(2), one O(3), and one O(8) atom. There are six inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), one O(5), and one O(6) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one W(1)O6 octahedra and  an edgeedge with one W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 46°. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(5), one O(6), one O(8), and one O(9) atom. In the fifth Lu site, Lu(5) is bonded in a 6-coordinate geometry to one O(10), one O(12), one O(4), one O(6), one O(7), and one O(8) atom. In the sixth Lu site, Lu(6) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(11), one O(12), one O(3), one O(7), and one O(8) atom. W(1) is bonded to one O(1), one O(11), one O(12), one O(2), one O(4), and one O(9) atom to form WO6 octahedra that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(2), one Lu(6), and one W(1) atom to form OLu3W tetrahedra that share corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), one Lu(1), one Lu(2), one Lu(3), and one Lu(6) atom to form distorted OLu4Mg trigonal bipyramids that share  a cornercorner with one O(1)Lu3W tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra,  a cornercorner with one O(7)Lu4 tetrahedra, corners with two equivalent O(6)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(5)Lu4 tetrahedra,  an edgeedge with one O(7)Lu4 tetrahedra, and  an edgeedge with one O(12)Lu3MgW trigonal bipyramid. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Lu(2), one Lu(3), one Lu(5), and one W(1) atom. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), one Lu(3), and one Lu(4) atom to form OLu4 tetrahedra that share  a cornercorner with one O(6)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the sixth O site, O(6) is bonded to one Lu(1), one Lu(2), one Lu(4), and one Lu(5) atom to form OLu4 tetrahedra that share  a cornercorner with one O(10)Lu4 tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra, corners with two equivalent O(12)Lu3MgW trigonal bipyramids, corners with two equivalent O(3)Lu4Mg trigonal bipyramids,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(5)Lu4 tetrahedra, and  an edgeedge with one O(7)Lu4 tetrahedra. In the seventh O site, O(7) is bonded to one Lu(2), one Lu(3), one Lu(5), and one Lu(6) atom to form OLu4 tetrahedra that share corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(10)Lu4 tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Mg(1), one Lu(3), one Lu(4), one Lu(5), and one Lu(6) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Lu(2), one Lu(4), and one W(1) atom. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(4), one Lu(5), and one Lu(6) atom to form distorted OLu4 tetrahedra that share  a cornercorner with one O(6)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W tetrahedra, corners with two equivalent O(5)Lu4 tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra,  a cornercorner with one O(12)Lu3MgW trigonal bipyramid,  an edgeedge with one O(6)Lu4 tetrahedra,  an edgeedge with one O(12)Lu3MgW trigonal bipyramid, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(4), one Lu(6), and one W(1) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Lu(1), one Lu(5), one Lu(6), and one W(1) atom to form distorted OLu3MgW trigonal bipyramids that share  a cornercorner with one O(1)Lu3W tetrahedra,  a cornercorner with one O(10)Lu4 tetrahedra,  a cornercorner with one O(5)Lu4 tetrahedra, corners with two equivalent O(6)Lu4 tetrahedra,  a cornercorner with one O(3)Lu4Mg trigonal bipyramid,  an edgeedge with one O(1)Lu3W tetrahedra,  an edgeedge with one O(10)Lu4 tetrahedra,  an edgeedge with one O(7)Lu4 tetrahedra, and  an edgeedge with one O(3)Lu4Mg trigonal bipyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu6MgWO12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.538
_cell_length_b   6.299
_cell_length_c   6.546
_cell_angle_alpha   97.769
_cell_angle_beta   100.393
_cell_angle_gamma   98.999
_symmetry_Int_Tables_number   1
_cell_volume   258.165
_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
  Lu  Lu0  1  0.126  0.306  0.635  1.0
  Lu  Lu1  1  0.396  0.862  0.691  1.0
  Lu  Lu2  1  0.346  0.609  0.149  1.0
  Lu  Lu3  1  0.655  0.396  0.825  1.0
  Lu  Lu4  1  0.575  0.139  0.325  1.0
  Lu  Lu5  1  0.870  0.739  0.414  1.0
  Mg  Mg6  1  0.938  0.369  0.193  1.0
  W  W7  1  0.999  0.974  0.992  1.0
  O  O8  1  0.071  0.938  0.689  1.0
  O  O9  1  0.109  0.305  0.979  1.0
  O  O10  1  0.164  0.570  0.410  1.0
  O  O11  1  0.315  0.939  0.080  1.0
  O  O12  1  0.397  0.568  0.822  1.0
  O  O13  1  0.409  0.184  0.575  1.0
  O  O14  1  0.567  0.816  0.427  1.0
  O  O15  1  0.621  0.423  0.172  1.0
  O  O16  1  0.705  0.057  0.890  1.0
  O  O17  1  0.822  0.427  0.578  1.0
  O  O18  1  0.913  0.671  0.057  1.0
  O  O19  1  0.921  0.084  0.306  1.0
[/CIF]
.