The structure described by Zr3Yb4O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to one O(1), one O(2), one O(4), two equivalent O(3), and two equivalent O(5) atoms to form distorted YbO7 pentagonal bipyramids that share  a cornercorner with one Yb(2)O7 hexagonal pyramid,  a cornercorner with one Zr(1)O6 octahedra, edges with three equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the second Yb site, Yb(2) is bonded to one O(2), one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form distorted YbO7 hexagonal pyramids that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Yb(1)O7 pentagonal bipyramid, edges with two equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with three equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 57°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form ZrO6 octahedra that share corners with two equivalent Yb(2)O7 hexagonal pyramids, corners with two equivalent Yb(1)O7 pentagonal bipyramids, edges with two equivalent Yb(2)O7 hexagonal pyramids, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(6), two equivalent O(2), and two equivalent O(4) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Yb(1), two equivalent Yb(2), and one Zr(2) atom to form OYb3Zr tetrahedra that share corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid. In the second O site, O(2) is bonded to one Yb(1), one Yb(2), and two equivalent Zr(2) atoms to form distorted OYb2Zr2 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the third O site, O(3) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(2) atom to form distorted OYb3Zr tetrahedra that share corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Yb(1), one Zr(1), and two equivalent Zr(2) atoms to form distorted OYbZr3 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra,  a cornercorner with one O(4)YbZr3 trigonal pyramid, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(1) atom to form distorted OYb3Zr tetrahedra that share  a cornercorner with one O(5)Yb3Zr tetrahedra, corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the sixth O site, O(6) is bonded to two equivalent Yb(2), one Zr(1), and one Zr(2) atom to form OYb2Zr2 tetrahedra that share  a cornercorner with one O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(2)Yb2Zr2 trigonal pyramids, corners with two equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. is represented by the CIF file [CIF]
data_Yb4Zr3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.383
_cell_length_b   6.408
_cell_length_c   6.532
_cell_angle_alpha   97.676
_cell_angle_beta   99.305
_cell_angle_gamma   100.640
_symmetry_Int_Tables_number   1
_cell_volume   255.426
_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
  Yb  Yb0  1  0.854  0.387  0.699  1.0
  Yb  Yb1  1  0.395  0.706  0.868  1.0
  Yb  Yb2  1  0.146  0.613  0.301  1.0
  Yb  Yb3  1  0.605  0.294  0.132  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.716  0.864  0.385  1.0
  Zr  Zr6  1  0.284  0.136  0.615  1.0
  O  O7  1  0.468  0.601  0.200  1.0
  O  O8  1  0.556  0.151  0.437  1.0
  O  O9  1  0.189  0.425  0.584  1.0
  O  O10  1  0.532  0.399  0.800  1.0
  O  O11  1  0.444  0.849  0.563  1.0
  O  O12  1  0.811  0.575  0.416  1.0
  O  O13  1  0.927  0.035  0.676  1.0
  O  O14  1  0.050  0.682  0.945  1.0
  O  O15  1  0.691  0.940  0.080  1.0
  O  O16  1  0.073  0.965  0.324  1.0
  O  O17  1  0.950  0.318  0.055  1.0
  O  O18  1  0.309  0.060  0.920  1.0
[/CIF]
.
The structure described by Zr3Yb4O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to one O(1), one O(2), one O(4), two equivalent O(3), and two equivalent O(5) atoms to form distorted YbO7 pentagonal bipyramids that share  a cornercorner with one Yb(2)O7 hexagonal pyramid,  a cornercorner with one Zr(1)O6 octahedra, edges with three equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the second Yb site, Yb(2) is bonded to one O(2), one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form distorted YbO7 hexagonal pyramids that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Yb(1)O7 pentagonal bipyramid, edges with two equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with three equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 57°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form ZrO6 octahedra that share corners with two equivalent Yb(2)O7 hexagonal pyramids, corners with two equivalent Yb(1)O7 pentagonal bipyramids, edges with two equivalent Yb(2)O7 hexagonal pyramids, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(6), two equivalent O(2), and two equivalent O(4) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Yb(1), two equivalent Yb(2), and one Zr(2) atom to form OYb3Zr tetrahedra that share corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid. In the second O site, O(2) is bonded to one Yb(1), one Yb(2), and two equivalent Zr(2) atoms to form distorted OYb2Zr2 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the third O site, O(3) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(2) atom to form distorted OYb3Zr tetrahedra that share corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Yb(1), one Zr(1), and two equivalent Zr(2) atoms to form distorted OYbZr3 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra,  a cornercorner with one O(4)YbZr3 trigonal pyramid, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(1) atom to form distorted OYb3Zr tetrahedra that share  a cornercorner with one O(5)Yb3Zr tetrahedra, corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the sixth O site, O(6) is bonded to two equivalent Yb(2), one Zr(1), and one Zr(2) atom to form OYb2Zr2 tetrahedra that share  a cornercorner with one O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(2)Yb2Zr2 trigonal pyramids, corners with two equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. is represented by the CIF file [CIF]
data_Yb4Zr3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.383
_cell_length_b   6.408
_cell_length_c   6.532
_cell_angle_alpha   97.676
_cell_angle_beta   99.305
_cell_angle_gamma   100.640
_symmetry_Int_Tables_number   1
_cell_volume   255.426
_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
  Yb  Yb0  1  0.854  0.387  0.699  1.0
  Yb  Yb1  1  0.395  0.706  0.868  1.0
  Yb  Yb2  1  0.146  0.613  0.301  1.0
  Yb  Yb3  1  0.605  0.294  0.132  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.716  0.864  0.385  1.0
  Zr  Zr6  1  0.284  0.136  0.615  1.0
  O  O7  1  0.468  0.601  0.200  1.0
  O  O8  1  0.556  0.151  0.437  1.0
  O  O9  1  0.189  0.425  0.584  1.0
  O  O10  1  0.532  0.399  0.800  1.0
  O  O11  1  0.444  0.849  0.563  1.0
  O  O12  1  0.811  0.575  0.416  1.0
  O  O13  1  0.927  0.035  0.676  1.0
  O  O14  1  0.050  0.682  0.945  1.0
  O  O15  1  0.691  0.940  0.080  1.0
  O  O16  1  0.073  0.965  0.324  1.0
  O  O17  1  0.950  0.318  0.055  1.0
  O  O18  1  0.309  0.060  0.920  1.0
[/CIF]
.