The structure described by LiBa4(RhO3)4 crystallizes in the trigonal P3m1 space group. Li(1) is bonded in a trigonal planar geometry to three equivalent O(1) atoms. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra,  a faceface with one Rh(1)O6 octahedra,  a faceface with one Rh(4)O6 octahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(3)O6 octahedra. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(3) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(4) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Li(1), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom to form a mixture of distorted corner and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 6-60°. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(4), one Rh(1), and one Rh(3) atom. is represented by the CIF file [CIF]
data_Ba4Li(RhO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.812
_cell_length_b   5.812
_cell_length_c   10.064
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   294.428
_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  0.667  0.333  0.750  1.0
  Ba  Ba1  1  0.333  0.667  0.251  1.0
  Ba  Ba2  1  0.000  0.000  0.455  1.0
  Ba  Ba3  1  0.000  0.000  0.045  1.0
  Li  Li4  1  0.000  0.000  0.751  1.0
  Rh  Rh5  1  0.333  0.667  0.887  1.0
  Rh  Rh6  1  0.667  0.333  0.387  1.0
  Rh  Rh7  1  0.667  0.333  0.113  1.0
  Rh  Rh8  1  0.333  0.667  0.614  1.0
  O  O9  1  0.182  0.364  0.750  1.0
  O  O10  1  0.818  0.182  0.250  1.0
  O  O11  1  0.365  0.182  0.250  1.0
  O  O12  1  0.636  0.818  0.750  1.0
  O  O13  1  0.182  0.818  0.750  1.0
  O  O14  1  0.818  0.635  0.250  1.0
  O  O15  1  0.496  0.992  0.494  1.0
  O  O16  1  0.496  0.504  0.006  1.0
  O  O17  1  0.496  0.993  0.006  1.0
  O  O18  1  0.496  0.504  0.494  1.0
  O  O19  1  0.008  0.504  0.494  1.0
  O  O20  1  0.007  0.504  0.006  1.0
[/CIF]
.
The structure described by LiBa4(RhO3)4 crystallizes in the trigonal P3m1 space group. Li(1) is bonded in a trigonal planar geometry to three equivalent O(1) atoms. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra,  a faceface with one Rh(1)O6 octahedra,  a faceface with one Rh(4)O6 octahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(3)O6 octahedra. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(3) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(4) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Li(1), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom to form a mixture of distorted corner and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 6-60°. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(4), one Rh(1), and one Rh(3) atom. is represented by the CIF file [CIF]
data_Ba4Li(RhO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.812
_cell_length_b   5.812
_cell_length_c   10.064
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   294.428
_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  0.667  0.333  0.750  1.0
  Ba  Ba1  1  0.333  0.667  0.251  1.0
  Ba  Ba2  1  0.000  0.000  0.455  1.0
  Ba  Ba3  1  0.000  0.000  0.045  1.0
  Li  Li4  1  0.000  0.000  0.751  1.0
  Rh  Rh5  1  0.333  0.667  0.887  1.0
  Rh  Rh6  1  0.667  0.333  0.387  1.0
  Rh  Rh7  1  0.667  0.333  0.113  1.0
  Rh  Rh8  1  0.333  0.667  0.614  1.0
  O  O9  1  0.182  0.364  0.750  1.0
  O  O10  1  0.818  0.182  0.250  1.0
  O  O11  1  0.365  0.182  0.250  1.0
  O  O12  1  0.636  0.818  0.750  1.0
  O  O13  1  0.182  0.818  0.750  1.0
  O  O14  1  0.818  0.635  0.250  1.0
  O  O15  1  0.496  0.992  0.494  1.0
  O  O16  1  0.496  0.504  0.006  1.0
  O  O17  1  0.496  0.993  0.006  1.0
  O  O18  1  0.496  0.504  0.494  1.0
  O  O19  1  0.008  0.504  0.494  1.0
  O  O20  1  0.007  0.504  0.006  1.0
[/CIF]
.