The structure described by Lu2O3 crystallizes in the monoclinic C2/m space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to two equivalent O(2), two equivalent O(4), and three equivalent O(1) atoms. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(5), two equivalent O(2), and three equivalent O(3) atoms. In the third Lu site, Lu(3) is bonded to one O(2), one O(3), two equivalent O(4), and two equivalent O(5) atoms to form a mixture of distorted corner and edge-sharing LuO6 octahedra. The corner-sharing octahedra are not tilted. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Lu(2) and three equivalent Lu(1) atoms to form distorted OLu4 trigonal pyramids that share  a cornercorner with one O(5)Lu6 octahedra, corners with three equivalent O(3)Lu4 tetrahedra, corners with six equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(2)Lu5 trigonal bipyramids, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with three equivalent O(2)Lu5 trigonal bipyramids, and edges with two equivalent O(1)Lu4 trigonal pyramids. The corner-sharing octahedral tilt angles are 38°. In the second O site, O(2) is bonded to one Lu(3), two equivalent Lu(1), and two equivalent Lu(2) atoms to form distorted OLu5 trigonal bipyramids that share corners with two equivalent O(4)Lu4 tetrahedra, corners with five equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra,  an edgeedge with one O(3)Lu4 tetrahedra, edges with two equivalent O(4)Lu4 tetrahedra, edges with two equivalent O(2)Lu5 trigonal bipyramids, and edges with three equivalent O(1)Lu4 trigonal pyramids. In the third O site, O(3) is bonded to one Lu(3) and three equivalent Lu(2) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(5)Lu6 octahedra, corners with two equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra, corners with five equivalent O(2)Lu5 trigonal bipyramids, corners with three equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra, edges with two equivalent O(3)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 49°. In the fourth O site, O(4) is bonded to two equivalent Lu(1) and two equivalent Lu(3) atoms to form OLu4 tetrahedra that share corners with two equivalent O(5)Lu6 octahedra, corners with two equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(2)Lu5 trigonal bipyramids, corners with six equivalent O(1)Lu4 trigonal pyramids,  an edgeedge with one O(5)Lu6 octahedra,  an edgeedge with one O(4)Lu4 tetrahedra, and edges with two equivalent O(2)Lu5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the fifth O site, O(5) is bonded to two equivalent Lu(2) and four equivalent Lu(3) atoms to form OLu6 octahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra, edges with two equivalent O(4)Lu4 tetrahedra, edges with four equivalent O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu5 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.359
_cell_length_b   7.007
_cell_length_c   8.333
_cell_angle_alpha   100.006
_cell_angle_beta   90.000
_cell_angle_gamma   103.867
_symmetry_Int_Tables_number   1
_cell_volume   187.338
_cell_formula_units_Z   3
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  0.365  0.729  0.513  1.0
  Lu  Lu1  1  0.691  0.383  0.137  1.0
  Lu  Lu2  1  0.968  0.935  0.186  1.0
  Lu  Lu3  1  0.635  0.271  0.487  1.0
  Lu  Lu4  1  0.032  0.065  0.814  1.0
  Lu  Lu5  1  0.309  0.617  0.863  1.0
  O  O6  1  0.793  0.585  0.377  1.0
  O  O7  1  0.873  0.746  0.719  1.0
  O  O8  1  0.826  0.651  0.032  1.0
  O  O9  1  0.530  0.061  0.657  1.0
  O  O10  1  0.174  0.349  0.968  1.0
  O  O11  1  0.127  0.254  0.281  1.0
  O  O12  1  0.207  0.415  0.623  1.0
  O  O13  1  0.500  0.000  0.000  1.0
  O  O14  1  0.470  0.939  0.343  1.0
[/CIF]
.
The structure described by Lu2O3 crystallizes in the monoclinic C2/m space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to two equivalent O(2), two equivalent O(4), and three equivalent O(1) atoms. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(5), two equivalent O(2), and three equivalent O(3) atoms. In the third Lu site, Lu(3) is bonded to one O(2), one O(3), two equivalent O(4), and two equivalent O(5) atoms to form a mixture of distorted corner and edge-sharing LuO6 octahedra. The corner-sharing octahedra are not tilted. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Lu(2) and three equivalent Lu(1) atoms to form distorted OLu4 trigonal pyramids that share  a cornercorner with one O(5)Lu6 octahedra, corners with three equivalent O(3)Lu4 tetrahedra, corners with six equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(2)Lu5 trigonal bipyramids, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with three equivalent O(2)Lu5 trigonal bipyramids, and edges with two equivalent O(1)Lu4 trigonal pyramids. The corner-sharing octahedral tilt angles are 38°. In the second O site, O(2) is bonded to one Lu(3), two equivalent Lu(1), and two equivalent Lu(2) atoms to form distorted OLu5 trigonal bipyramids that share corners with two equivalent O(4)Lu4 tetrahedra, corners with five equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra,  an edgeedge with one O(3)Lu4 tetrahedra, edges with two equivalent O(4)Lu4 tetrahedra, edges with two equivalent O(2)Lu5 trigonal bipyramids, and edges with three equivalent O(1)Lu4 trigonal pyramids. In the third O site, O(3) is bonded to one Lu(3) and three equivalent Lu(2) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(5)Lu6 octahedra, corners with two equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra, corners with five equivalent O(2)Lu5 trigonal bipyramids, corners with three equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra, edges with two equivalent O(3)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 49°. In the fourth O site, O(4) is bonded to two equivalent Lu(1) and two equivalent Lu(3) atoms to form OLu4 tetrahedra that share corners with two equivalent O(5)Lu6 octahedra, corners with two equivalent O(3)Lu4 tetrahedra, corners with two equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(2)Lu5 trigonal bipyramids, corners with six equivalent O(1)Lu4 trigonal pyramids,  an edgeedge with one O(5)Lu6 octahedra,  an edgeedge with one O(4)Lu4 tetrahedra, and edges with two equivalent O(2)Lu5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the fifth O site, O(5) is bonded to two equivalent Lu(2) and four equivalent Lu(3) atoms to form OLu6 octahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(1)Lu4 trigonal pyramids, edges with two equivalent O(5)Lu6 octahedra, edges with two equivalent O(4)Lu4 tetrahedra, edges with four equivalent O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu5 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.359
_cell_length_b   7.007
_cell_length_c   8.333
_cell_angle_alpha   100.006
_cell_angle_beta   90.000
_cell_angle_gamma   103.867
_symmetry_Int_Tables_number   1
_cell_volume   187.338
_cell_formula_units_Z   3
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  0.365  0.729  0.513  1.0
  Lu  Lu1  1  0.691  0.383  0.137  1.0
  Lu  Lu2  1  0.968  0.935  0.186  1.0
  Lu  Lu3  1  0.635  0.271  0.487  1.0
  Lu  Lu4  1  0.032  0.065  0.814  1.0
  Lu  Lu5  1  0.309  0.617  0.863  1.0
  O  O6  1  0.793  0.585  0.377  1.0
  O  O7  1  0.873  0.746  0.719  1.0
  O  O8  1  0.826  0.651  0.032  1.0
  O  O9  1  0.530  0.061  0.657  1.0
  O  O10  1  0.174  0.349  0.968  1.0
  O  O11  1  0.127  0.254  0.281  1.0
  O  O12  1  0.207  0.415  0.623  1.0
  O  O13  1  0.500  0.000  0.000  1.0
  O  O14  1  0.470  0.939  0.343  1.0
[/CIF]
.