The compound described by Lu10Ti6O27 crystallizes in the monoclinic Cm space group. There are eight inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), one O(7), one O(8), two equivalent O(10), and two equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Ti(4)O6 octahedra and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles are 71°. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(15), one O(4), two equivalent O(13), and two equivalent O(3) atoms. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(1), one O(12), two equivalent O(10), and two equivalent O(2) atoms. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(1), one O(18), two equivalent O(13), and two equivalent O(3) atoms. In the fifth Lu site, Lu(5) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. In the sixth Lu site, Lu(6) is bonded to one O(11), one O(18), one O(19), two equivalent O(17), and two equivalent O(6) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(8)O7 hexagonal pyramid, corners with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the seventh Lu site, Lu(7) is bonded in a 7-coordinate geometry to one O(11), one O(13), one O(14), one O(15), one O(17), one O(18), and one O(9) atom. In the eighth Lu site, Lu(8) is bonded to one O(11), one O(12), one O(16), two equivalent O(5), and two equivalent O(9) atoms to form distorted LuO7 hexagonal pyramids that share corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Lu(6)O7 pentagonal bipyramid, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(13), one O(19), one O(3), and one O(6) atom. In the second Ti site, Ti(2) is bonded to one O(16), one O(17), one O(2), one O(5), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Lu(8)O7 hexagonal pyramid,  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Lu(6)O7 pentagonal bipyramid,  an edgeedge with one Lu(8)O7 hexagonal pyramid, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 32-62°. In the third Ti site, Ti(3) is bonded to one O(14), one O(15), two equivalent O(17), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share  a cornercorner with one Ti(4)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Lu(6)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 49-62°. In the fourth Ti site, Ti(4) is bonded to one O(14), one O(8), two equivalent O(5), and two equivalent O(9) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, and edges with two equivalent Lu(8)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 49-54°. There are nineteen inequivalent O sites. In the first O site, O(1) is bonded to one Lu(3), one Lu(4), and two equivalent Ti(1) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with four equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(10)Lu3Ti tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), one Lu(3), one Lu(5), and one Ti(2) atom to form distorted OLu3Ti trigonal pyramids that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra,  a cornercorner with one O(17)Lu2Ti2 tetrahedra,  a cornercorner with one O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(3)Lu3Ti tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra, corners with two equivalent O(12)Lu4 tetrahedra, corners with three equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(10)Lu3Ti tetrahedra, and  an edgeedge with one O(4)Lu4 tetrahedra. In the third O site, O(3) is bonded to one Lu(2), one Lu(4), one Lu(5), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra,  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with two equivalent O(1)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra,  a cornercorner with one O(2)Lu3Ti trigonal pyramid, corners with three equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(10)Lu3Ti tetrahedra,  an edgeedge with one O(4)Lu4 tetrahedra, and  an edgeedge with one O(13)Lu3Ti trigonal pyramid. In the fourth O site, O(4) is bonded to one Lu(1), one Lu(2), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra, corners with three equivalent O(8)Lu3Ti tetrahedra, corners with four equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(12)Lu4 tetrahedra, edges with two equivalent O(3)Lu3Ti tetrahedra, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Lu(5), one Lu(8), one Ti(2), and one Ti(4) atom. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Lu(6), one Ti(1), and one Ti(3) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Lu(1) and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded to one Lu(1), two equivalent Lu(5), and one Ti(4) atom to form OLu3Ti tetrahedra that share corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(12)Lu4 tetrahedra, corners with three equivalent O(4)Lu4 tetrahedra, corners with four equivalent O(2)Lu3Ti trigonal pyramids, and edges with two equivalent O(10)Lu3Ti tetrahedra. In the ninth O site, O(9) is bonded to one Lu(7), one Lu(8), one Ti(2), and one Ti(4) atom to form distorted OLu2Ti2 tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra,  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid,  a cornercorner with one O(2)Lu3Ti trigonal pyramid,  an edgeedge with one O(17)Lu2Ti2 tetrahedra, and  an edgeedge with one O(11)Lu4 tetrahedra. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(3), one Lu(5), and one Ti(1) atom to form distorted OLu3Ti tetrahedra that share corners with two equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(1)Lu2Ti2 tetrahedra,  an edgeedge with one O(3)Lu3Ti tetrahedra,  an edgeedge with one O(8)Lu3Ti tetrahedra,  an edgeedge with one O(12)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Ti trigonal pyramid. In the eleventh O site, O(11) is bonded to one Lu(6), one Lu(8), and two equivalent Lu(7) atoms to form distorted OLu4 tetrahedra that share  a cornercorner with one O(12)Lu4 tetrahedra, corners with three equivalent O(18)Lu4 tetrahedra, corners with four equivalent O(17)Lu2Ti2 tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(15)Lu3Ti tetrahedra, and edges with two equivalent O(9)Lu2Ti2 tetrahedra. In the twelfth O site, O(12) is bonded to one Lu(3), one Lu(8), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra,  a cornercorner with one O(11)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra, corners with four equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(4)Lu4 tetrahedra, and edges with two equivalent O(10)Lu3Ti tetrahedra. In the thirteenth O site, O(13) is bonded to one Lu(2), one Lu(4), one Lu(7), and one Ti(1) atom to form distorted OLu3Ti trigonal pyramids that share  a cornercorner with one O(17)Lu2Ti2 tetrahedra,  a cornercorner with one O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(10)Lu3Ti tetrahedra,  a cornercorner with one O(11)Lu4 tetrahedra,  a cornercorner with one O(4)Lu4 tetrahedra, corners with three equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(1)Lu2Ti2 tetrahedra,  an edgeedge with one O(15)Lu3Ti tetrahedra,  an edgeedge with one O(3)Lu3Ti tetrahedra, and  an edgeedge with one O(18)Lu4 tetrahedra. In the fourteenth O site, O(14) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Lu(7), one Ti(3), and one Ti(4) atom. In the fifteenth O site, O(15) is bonded to one Lu(2), two equivalent Lu(7), and one Ti(3) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(4)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(18)Lu4 tetrahedra,  an edgeedge with one O(11)Lu4 tetrahedra, edges with two equivalent O(17)Lu2Ti2 tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Lu(8) and two equivalent Ti(2) atoms. In the seventeenth O site, O(17) is bonded to one Lu(6), one Lu(7), one Ti(2), and one Ti(3) atom to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(17)Lu2Ti2 tetrahedra, corners with two equivalent O(11)Lu4 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid,  a cornercorner with one O(2)Lu3Ti trigonal pyramid,  an edgeedge with one O(9)Lu2Ti2 tetrahedra,  an edgeedge with one O(15)Lu3Ti tetrahedra, and  an edgeedge with one O(18)Lu4 tetrahedra. In the eighteenth O site, O(18) is bonded to one Lu(4), one Lu(6), and two equivalent Lu(7) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(15)Lu3Ti tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with three equivalent O(11)Lu4 tetrahedra, edges with two equivalent O(17)Lu2Ti2 tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one Lu(6) and two equivalent Ti(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu10Ti6O27
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.315
_cell_length_b   7.315
_cell_length_c   12.280
_cell_angle_alpha   72.438
_cell_angle_beta   72.438
_cell_angle_gamma   58.533
_symmetry_Int_Tables_number   1
_cell_volume   525.912
_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  0.259  0.259  0.270  1.0
  Lu  Lu1  1  0.517  0.517  0.995  1.0
  Lu  Lu2  1  0.744  0.744  0.238  1.0
  Lu  Lu3  1  0.984  0.984  0.990  1.0
  Lu  Lu4  1  0.748  0.262  0.251  1.0
  Lu  Lu5  1  0.250  0.250  0.768  1.0
  Lu  Lu6  1  0.262  0.748  0.251  1.0
  Lu  Lu7  1  0.278  0.771  0.734  1.0
  Lu  Lu8  1  0.515  0.515  0.505  1.0
  Lu  Lu9  1  0.771  0.278  0.734  1.0
  Ti  Ti10  1  0.018  0.498  0.006  1.0
  Ti  Ti11  1  0.518  0.008  0.491  1.0
  Ti  Ti12  1  0.748  0.748  0.754  1.0
  Ti  Ti13  1  0.003  0.003  0.506  1.0
  Ti  Ti14  1  0.498  0.018  0.006  1.0
  Ti  Ti15  1  0.008  0.518  0.491  1.0
  O  O16  1  0.798  0.798  0.048  1.0
  O  O17  1  0.614  0.029  0.313  1.0
  O  O18  1  0.834  0.279  0.064  1.0
  O  O19  1  0.029  0.614  0.313  1.0
  O  O20  1  0.435  0.435  0.184  1.0
  O  O21  1  0.153  0.671  0.478  1.0
  O  O22  1  0.917  0.555  0.865  1.0
  O  O23  1  0.261  0.261  0.450  1.0
  O  O24  1  0.057  0.057  0.340  1.0
  O  O25  1  0.279  0.834  0.064  1.0
  O  O26  1  0.286  0.874  0.542  1.0
  O  O27  1  0.421  0.992  0.169  1.0
  O  O28  1  0.430  0.430  0.690  1.0
  O  O29  1  0.568  0.568  0.317  1.0
  O  O30  1  0.555  0.917  0.865  1.0
  O  O31  1  0.671  0.153  0.478  1.0
  O  O32  1  0.632  0.199  0.940  1.0
  O  O33  1  0.908  0.908  0.678  1.0
  O  O34  1  0.584  0.584  0.796  1.0
  O  O35  1  0.696  0.696  0.493  1.0
  O  O36  1  0.992  0.421  0.169  1.0
  O  O37  1  0.874  0.286  0.542  1.0
  O  O38  1  0.973  0.467  0.662  1.0
  O  O39  1  0.199  0.632  0.940  1.0
  O  O40  1  0.067  0.067  0.811  1.0
  O  O41  1  0.241  0.241  0.951  1.0
  O  O42  1  0.467  0.973  0.662  1.0
[/CIF]
.
The compound described by Lu10Ti6O27 crystallizes in the monoclinic Cm space group. There are eight inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), one O(7), one O(8), two equivalent O(10), and two equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Ti(4)O6 octahedra and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles are 71°. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(15), one O(4), two equivalent O(13), and two equivalent O(3) atoms. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(1), one O(12), two equivalent O(10), and two equivalent O(2) atoms. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(1), one O(18), two equivalent O(13), and two equivalent O(3) atoms. In the fifth Lu site, Lu(5) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. In the sixth Lu site, Lu(6) is bonded to one O(11), one O(18), one O(19), two equivalent O(17), and two equivalent O(6) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(8)O7 hexagonal pyramid, corners with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the seventh Lu site, Lu(7) is bonded in a 7-coordinate geometry to one O(11), one O(13), one O(14), one O(15), one O(17), one O(18), and one O(9) atom. In the eighth Lu site, Lu(8) is bonded to one O(11), one O(12), one O(16), two equivalent O(5), and two equivalent O(9) atoms to form distorted LuO7 hexagonal pyramids that share corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Lu(6)O7 pentagonal bipyramid, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(13), one O(19), one O(3), and one O(6) atom. In the second Ti site, Ti(2) is bonded to one O(16), one O(17), one O(2), one O(5), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Lu(8)O7 hexagonal pyramid,  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Lu(6)O7 pentagonal bipyramid,  an edgeedge with one Lu(8)O7 hexagonal pyramid, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 32-62°. In the third Ti site, Ti(3) is bonded to one O(14), one O(15), two equivalent O(17), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share  a cornercorner with one Ti(4)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Lu(6)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 49-62°. In the fourth Ti site, Ti(4) is bonded to one O(14), one O(8), two equivalent O(5), and two equivalent O(9) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, and edges with two equivalent Lu(8)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 49-54°. There are nineteen inequivalent O sites. In the first O site, O(1) is bonded to one Lu(3), one Lu(4), and two equivalent Ti(1) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with four equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(10)Lu3Ti tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), one Lu(3), one Lu(5), and one Ti(2) atom to form distorted OLu3Ti trigonal pyramids that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra,  a cornercorner with one O(17)Lu2Ti2 tetrahedra,  a cornercorner with one O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(3)Lu3Ti tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra, corners with two equivalent O(12)Lu4 tetrahedra, corners with three equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(10)Lu3Ti tetrahedra, and  an edgeedge with one O(4)Lu4 tetrahedra. In the third O site, O(3) is bonded to one Lu(2), one Lu(4), one Lu(5), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra,  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with two equivalent O(1)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra,  a cornercorner with one O(2)Lu3Ti trigonal pyramid, corners with three equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(10)Lu3Ti tetrahedra,  an edgeedge with one O(4)Lu4 tetrahedra, and  an edgeedge with one O(13)Lu3Ti trigonal pyramid. In the fourth O site, O(4) is bonded to one Lu(1), one Lu(2), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra, corners with three equivalent O(8)Lu3Ti tetrahedra, corners with four equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(12)Lu4 tetrahedra, edges with two equivalent O(3)Lu3Ti tetrahedra, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Lu(5), one Lu(8), one Ti(2), and one Ti(4) atom. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Lu(6), one Ti(1), and one Ti(3) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Lu(1) and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded to one Lu(1), two equivalent Lu(5), and one Ti(4) atom to form OLu3Ti tetrahedra that share corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(12)Lu4 tetrahedra, corners with three equivalent O(4)Lu4 tetrahedra, corners with four equivalent O(2)Lu3Ti trigonal pyramids, and edges with two equivalent O(10)Lu3Ti tetrahedra. In the ninth O site, O(9) is bonded to one Lu(7), one Lu(8), one Ti(2), and one Ti(4) atom to form distorted OLu2Ti2 tetrahedra that share  a cornercorner with one O(15)Lu3Ti tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra,  a cornercorner with one O(12)Lu4 tetrahedra,  a cornercorner with one O(18)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid,  a cornercorner with one O(2)Lu3Ti trigonal pyramid,  an edgeedge with one O(17)Lu2Ti2 tetrahedra, and  an edgeedge with one O(11)Lu4 tetrahedra. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(3), one Lu(5), and one Ti(1) atom to form distorted OLu3Ti tetrahedra that share corners with two equivalent O(10)Lu3Ti tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(1)Lu2Ti2 tetrahedra,  an edgeedge with one O(3)Lu3Ti tetrahedra,  an edgeedge with one O(8)Lu3Ti tetrahedra,  an edgeedge with one O(12)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Ti trigonal pyramid. In the eleventh O site, O(11) is bonded to one Lu(6), one Lu(8), and two equivalent Lu(7) atoms to form distorted OLu4 tetrahedra that share  a cornercorner with one O(12)Lu4 tetrahedra, corners with three equivalent O(18)Lu4 tetrahedra, corners with four equivalent O(17)Lu2Ti2 tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(15)Lu3Ti tetrahedra, and edges with two equivalent O(9)Lu2Ti2 tetrahedra. In the twelfth O site, O(12) is bonded to one Lu(3), one Lu(8), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra,  a cornercorner with one O(11)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra, corners with four equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(4)Lu4 tetrahedra, and edges with two equivalent O(10)Lu3Ti tetrahedra. In the thirteenth O site, O(13) is bonded to one Lu(2), one Lu(4), one Lu(7), and one Ti(1) atom to form distorted OLu3Ti trigonal pyramids that share  a cornercorner with one O(17)Lu2Ti2 tetrahedra,  a cornercorner with one O(9)Lu2Ti2 tetrahedra,  a cornercorner with one O(10)Lu3Ti tetrahedra,  a cornercorner with one O(11)Lu4 tetrahedra,  a cornercorner with one O(4)Lu4 tetrahedra, corners with three equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(13)Lu3Ti trigonal pyramids,  an edgeedge with one O(1)Lu2Ti2 tetrahedra,  an edgeedge with one O(15)Lu3Ti tetrahedra,  an edgeedge with one O(3)Lu3Ti tetrahedra, and  an edgeedge with one O(18)Lu4 tetrahedra. In the fourteenth O site, O(14) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Lu(7), one Ti(3), and one Ti(4) atom. In the fifteenth O site, O(15) is bonded to one Lu(2), two equivalent Lu(7), and one Ti(3) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(4)Lu4 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with two equivalent O(18)Lu4 tetrahedra,  an edgeedge with one O(11)Lu4 tetrahedra, edges with two equivalent O(17)Lu2Ti2 tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Lu(8) and two equivalent Ti(2) atoms. In the seventeenth O site, O(17) is bonded to one Lu(6), one Lu(7), one Ti(2), and one Ti(3) atom to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(17)Lu2Ti2 tetrahedra, corners with two equivalent O(11)Lu4 tetrahedra,  a cornercorner with one O(13)Lu3Ti trigonal pyramid,  a cornercorner with one O(2)Lu3Ti trigonal pyramid,  an edgeedge with one O(9)Lu2Ti2 tetrahedra,  an edgeedge with one O(15)Lu3Ti tetrahedra, and  an edgeedge with one O(18)Lu4 tetrahedra. In the eighteenth O site, O(18) is bonded to one Lu(4), one Lu(6), and two equivalent Lu(7) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(1)Lu2Ti2 tetrahedra, corners with two equivalent O(9)Lu2Ti2 tetrahedra, corners with two equivalent O(15)Lu3Ti tetrahedra, corners with two equivalent O(3)Lu3Ti tetrahedra, corners with three equivalent O(11)Lu4 tetrahedra, edges with two equivalent O(17)Lu2Ti2 tetrahedra, and edges with two equivalent O(13)Lu3Ti trigonal pyramids. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one Lu(6) and two equivalent Ti(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu10Ti6O27
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.315
_cell_length_b   7.315
_cell_length_c   12.280
_cell_angle_alpha   72.438
_cell_angle_beta   72.438
_cell_angle_gamma   58.533
_symmetry_Int_Tables_number   1
_cell_volume   525.912
_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  0.259  0.259  0.270  1.0
  Lu  Lu1  1  0.517  0.517  0.995  1.0
  Lu  Lu2  1  0.744  0.744  0.238  1.0
  Lu  Lu3  1  0.984  0.984  0.990  1.0
  Lu  Lu4  1  0.748  0.262  0.251  1.0
  Lu  Lu5  1  0.250  0.250  0.768  1.0
  Lu  Lu6  1  0.262  0.748  0.251  1.0
  Lu  Lu7  1  0.278  0.771  0.734  1.0
  Lu  Lu8  1  0.515  0.515  0.505  1.0
  Lu  Lu9  1  0.771  0.278  0.734  1.0
  Ti  Ti10  1  0.018  0.498  0.006  1.0
  Ti  Ti11  1  0.518  0.008  0.491  1.0
  Ti  Ti12  1  0.748  0.748  0.754  1.0
  Ti  Ti13  1  0.003  0.003  0.506  1.0
  Ti  Ti14  1  0.498  0.018  0.006  1.0
  Ti  Ti15  1  0.008  0.518  0.491  1.0
  O  O16  1  0.798  0.798  0.048  1.0
  O  O17  1  0.614  0.029  0.313  1.0
  O  O18  1  0.834  0.279  0.064  1.0
  O  O19  1  0.029  0.614  0.313  1.0
  O  O20  1  0.435  0.435  0.184  1.0
  O  O21  1  0.153  0.671  0.478  1.0
  O  O22  1  0.917  0.555  0.865  1.0
  O  O23  1  0.261  0.261  0.450  1.0
  O  O24  1  0.057  0.057  0.340  1.0
  O  O25  1  0.279  0.834  0.064  1.0
  O  O26  1  0.286  0.874  0.542  1.0
  O  O27  1  0.421  0.992  0.169  1.0
  O  O28  1  0.430  0.430  0.690  1.0
  O  O29  1  0.568  0.568  0.317  1.0
  O  O30  1  0.555  0.917  0.865  1.0
  O  O31  1  0.671  0.153  0.478  1.0
  O  O32  1  0.632  0.199  0.940  1.0
  O  O33  1  0.908  0.908  0.678  1.0
  O  O34  1  0.584  0.584  0.796  1.0
  O  O35  1  0.696  0.696  0.493  1.0
  O  O36  1  0.992  0.421  0.169  1.0
  O  O37  1  0.874  0.286  0.542  1.0
  O  O38  1  0.973  0.467  0.662  1.0
  O  O39  1  0.199  0.632  0.940  1.0
  O  O40  1  0.067  0.067  0.811  1.0
  O  O41  1  0.241  0.241  0.951  1.0
  O  O42  1  0.467  0.973  0.662  1.0
[/CIF]
.