The structure described by Ba3Yb4O9 crystallizes in the trigonal R3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(3) atoms. In the second Ba site, Ba(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(3) atoms. There are four inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. In the second Yb site, Yb(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form corner-sharing YbO6 octahedra. The corner-sharing octahedral tilt angles are 23°. In the third Yb site, Yb(3) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. In the fourth Yb site, Yb(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form corner-sharing YbO6 octahedra. The corner-sharing octahedral tilt angles are 23°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Yb(1), one Yb(3), and one Yb(4) atom to form distorted OBaYb3 tetrahedra that share corners with four equivalent O(1)BaYb3 tetrahedra, corners with four equivalent O(3)Ba3Yb2 trigonal bipyramids, edges with two equivalent O(1)BaYb3 tetrahedra, and  an edgeedge with one O(3)Ba3Yb2 trigonal bipyramid. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(3), one Yb(1), one Yb(2), and one Yb(3) atom. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), one Ba(3), one Yb(2), and one Yb(4) atom to form distorted OBa3Yb2 trigonal bipyramids that share corners with four equivalent O(1)BaYb3 tetrahedra, corners with two equivalent O(3)Ba3Yb2 trigonal bipyramids,  an edgeedge with one O(1)BaYb3 tetrahedra, and edges with four equivalent O(3)Ba3Yb2 trigonal bipyramids. is represented by the CIF file [CIF]
data_Ba3Yb4O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.039
_cell_length_b   9.039
_cell_length_c   9.039
_cell_angle_alpha   40.374
_cell_angle_beta   40.374
_cell_angle_gamma   40.374
_symmetry_Int_Tables_number   1
_cell_volume   279.384
_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
  Ba  Ba0  1  0.009  0.009  0.009  1.0
  Ba  Ba1  1  0.176  0.176  0.176  1.0
  Ba  Ba2  1  0.585  0.585  0.585  1.0
  Yb  Yb3  1  0.434  0.434  0.434  1.0
  Yb  Yb4  1  0.874  0.874  0.874  1.0
  Yb  Yb5  1  0.752  0.752  0.752  1.0
  Yb  Yb6  1  0.313  0.313  0.313  1.0
  O  O7  1  0.619  0.444  0.058  1.0
  O  O8  1  0.058  0.619  0.444  1.0
  O  O9  1  0.444  0.058  0.619  1.0
  O  O10  1  0.733  0.578  0.135  1.0
  O  O11  1  0.135  0.733  0.578  1.0
  O  O12  1  0.578  0.135  0.733  1.0
  O  O13  1  0.591  0.021  0.167  1.0
  O  O14  1  0.021  0.167  0.591  1.0
  O  O15  1  0.167  0.591  0.021  1.0
[/CIF]
.
The structure described by Ba3Yb4O9 crystallizes in the trigonal R3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(3) atoms. In the second Ba site, Ba(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(3) atoms. There are four inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. In the second Yb site, Yb(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form corner-sharing YbO6 octahedra. The corner-sharing octahedral tilt angles are 23°. In the third Yb site, Yb(3) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. In the fourth Yb site, Yb(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form corner-sharing YbO6 octahedra. The corner-sharing octahedral tilt angles are 23°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Yb(1), one Yb(3), and one Yb(4) atom to form distorted OBaYb3 tetrahedra that share corners with four equivalent O(1)BaYb3 tetrahedra, corners with four equivalent O(3)Ba3Yb2 trigonal bipyramids, edges with two equivalent O(1)BaYb3 tetrahedra, and  an edgeedge with one O(3)Ba3Yb2 trigonal bipyramid. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(3), one Yb(1), one Yb(2), and one Yb(3) atom. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), one Ba(3), one Yb(2), and one Yb(4) atom to form distorted OBa3Yb2 trigonal bipyramids that share corners with four equivalent O(1)BaYb3 tetrahedra, corners with two equivalent O(3)Ba3Yb2 trigonal bipyramids,  an edgeedge with one O(1)BaYb3 tetrahedra, and edges with four equivalent O(3)Ba3Yb2 trigonal bipyramids. is represented by the CIF file [CIF]
data_Ba3Yb4O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.039
_cell_length_b   9.039
_cell_length_c   9.039
_cell_angle_alpha   40.374
_cell_angle_beta   40.374
_cell_angle_gamma   40.374
_symmetry_Int_Tables_number   1
_cell_volume   279.384
_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
  Ba  Ba0  1  0.009  0.009  0.009  1.0
  Ba  Ba1  1  0.176  0.176  0.176  1.0
  Ba  Ba2  1  0.585  0.585  0.585  1.0
  Yb  Yb3  1  0.434  0.434  0.434  1.0
  Yb  Yb4  1  0.874  0.874  0.874  1.0
  Yb  Yb5  1  0.752  0.752  0.752  1.0
  Yb  Yb6  1  0.313  0.313  0.313  1.0
  O  O7  1  0.619  0.444  0.058  1.0
  O  O8  1  0.058  0.619  0.444  1.0
  O  O9  1  0.444  0.058  0.619  1.0
  O  O10  1  0.733  0.578  0.135  1.0
  O  O11  1  0.135  0.733  0.578  1.0
  O  O12  1  0.578  0.135  0.733  1.0
  O  O13  1  0.591  0.021  0.167  1.0
  O  O14  1  0.021  0.167  0.591  1.0
  O  O15  1  0.167  0.591  0.021  1.0
[/CIF]
.