The material structure described by Lu4Zr3O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(4), one O(5), two equivalent O(2), and two equivalent O(6) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Lu(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(2), one O(5), one O(6), two equivalent O(3), and two equivalent O(4) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form ZrO6 octahedra that share corners with two equivalent Lu(1)O7 pentagonal bipyramids and edges with two equivalent Lu(1)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(6), and two equivalent O(5) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Zr(1), and one Zr(2) atom. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(1) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(2)Lu3Zr tetrahedra, corners with two equivalent O(3)Lu2Zr2 tetrahedra, corners with two equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(2), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(3)Lu2Zr2 tetrahedra, corners with two equivalent O(5)Lu2Zr2 tetrahedra, corners with two equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra, and  an edgeedge with one O(4)Lu3Zr tetrahedra. In the fourth O site, O(4) is bonded to one Lu(1), two equivalent Lu(2), and one Zr(2) atom to form OLu3Zr tetrahedra that share corners with two equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), and two equivalent Zr(2) atoms to form OLu2Zr2 tetrahedra that share corners with two equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(2) atom to form distorted OLu3Zr tetrahedra that share corners with three equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu4Zr3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.250
_cell_length_b   6.259
_cell_length_c   6.367
_cell_angle_alpha   99.639
_cell_angle_beta   99.066
_cell_angle_gamma   99.468
_symmetry_Int_Tables_number   1
_cell_volume   237.779
_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  0.391  0.698  0.864  1.0
  Lu  Lu1  1  0.690  0.863  0.390  1.0
  Lu  Lu2  1  0.609  0.302  0.136  1.0
  Lu  Lu3  1  0.310  0.137  0.610  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.852  0.394  0.678  1.0
  Zr  Zr6  1  0.148  0.606  0.322  1.0
  O  O7  1  0.040  0.676  0.898  1.0
  O  O8  1  0.683  0.926  0.060  1.0
  O  O9  1  0.917  0.075  0.686  1.0
  O  O10  1  0.960  0.324  0.102  1.0
  O  O11  1  0.317  0.074  0.940  1.0
  O  O12  1  0.083  0.925  0.314  1.0
  O  O13  1  0.584  0.185  0.431  1.0
  O  O14  1  0.175  0.427  0.574  1.0
  O  O15  1  0.416  0.579  0.178  1.0
  O  O16  1  0.416  0.815  0.569  1.0
  O  O17  1  0.825  0.573  0.426  1.0
  O  O18  1  0.584  0.421  0.822  1.0
[/CIF]
.
The material structure described by Lu4Zr3O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(4), one O(5), two equivalent O(2), and two equivalent O(6) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Lu(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(2), one O(5), one O(6), two equivalent O(3), and two equivalent O(4) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form ZrO6 octahedra that share corners with two equivalent Lu(1)O7 pentagonal bipyramids and edges with two equivalent Lu(1)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(6), and two equivalent O(5) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Zr(1), and one Zr(2) atom. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(1) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(2)Lu3Zr tetrahedra, corners with two equivalent O(3)Lu2Zr2 tetrahedra, corners with two equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(2), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(3)Lu2Zr2 tetrahedra, corners with two equivalent O(5)Lu2Zr2 tetrahedra, corners with two equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra, and  an edgeedge with one O(4)Lu3Zr tetrahedra. In the fourth O site, O(4) is bonded to one Lu(1), two equivalent Lu(2), and one Zr(2) atom to form OLu3Zr tetrahedra that share corners with two equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), and two equivalent Zr(2) atoms to form OLu2Zr2 tetrahedra that share corners with two equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra, corners with three equivalent O(6)Lu3Zr tetrahedra,  an edgeedge with one O(3)Lu2Zr2 tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(2) atom to form distorted OLu3Zr tetrahedra that share corners with three equivalent O(3)Lu2Zr2 tetrahedra, corners with three equivalent O(5)Lu2Zr2 tetrahedra, corners with three equivalent O(2)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu3Zr tetrahedra,  an edgeedge with one O(5)Lu2Zr2 tetrahedra,  an edgeedge with one O(2)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu3Zr tetrahedra, and  an edgeedge with one O(6)Lu3Zr tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu4Zr3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.250
_cell_length_b   6.259
_cell_length_c   6.367
_cell_angle_alpha   99.639
_cell_angle_beta   99.066
_cell_angle_gamma   99.468
_symmetry_Int_Tables_number   1
_cell_volume   237.779
_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  0.391  0.698  0.864  1.0
  Lu  Lu1  1  0.690  0.863  0.390  1.0
  Lu  Lu2  1  0.609  0.302  0.136  1.0
  Lu  Lu3  1  0.310  0.137  0.610  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.852  0.394  0.678  1.0
  Zr  Zr6  1  0.148  0.606  0.322  1.0
  O  O7  1  0.040  0.676  0.898  1.0
  O  O8  1  0.683  0.926  0.060  1.0
  O  O9  1  0.917  0.075  0.686  1.0
  O  O10  1  0.960  0.324  0.102  1.0
  O  O11  1  0.317  0.074  0.940  1.0
  O  O12  1  0.083  0.925  0.314  1.0
  O  O13  1  0.584  0.185  0.431  1.0
  O  O14  1  0.175  0.427  0.574  1.0
  O  O15  1  0.416  0.579  0.178  1.0
  O  O16  1  0.416  0.815  0.569  1.0
  O  O17  1  0.825  0.573  0.426  1.0
  O  O18  1  0.584  0.421  0.822  1.0
[/CIF]
.