The compound described by LiGd6In2O12 crystallizes in the trigonal R3 space group. Li(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted LiO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids,  a faceface with one In(1)O6 octahedra,  a faceface with one In(2)O6 octahedra, and faces with three equivalent Gd(1)O6 pentagonal pyramids. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form distorted GdO6 pentagonal pyramids that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one In(1)O6 octahedra,  a cornercorner with one In(2)O6 octahedra, corners with four equivalent Gd(1)O6 pentagonal pyramids,  an edgeedge with one In(1)O6 octahedra,  an edgeedge with one In(2)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 35-38°. In the second Gd site, Gd(2) is bonded in a 6-coordinate geometry to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms. There are two inequivalent In sites. In the first In site, In(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted InO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids, edges with three equivalent Gd(1)O6 pentagonal pyramids, and  a faceface with one Li(1)O6 octahedra. In the second In site, In(2) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form InO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids, edges with three equivalent Gd(1)O6 pentagonal pyramids, and  a faceface with one Li(1)O6 octahedra. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted see-saw-like geometry to one Gd(1), two equivalent Gd(2), and one In(2) atom. In the second O site, O(1) is bonded to one Gd(1), two equivalent Gd(2), and one In(1) atom to form OGd3In trigonal pyramids that share corners with two equivalent O(3)LiGd3In square pyramids,  a cornercorner with one O(2)LiGd3In trigonal bipyramid, corners with four equivalent O(1)Gd3In trigonal pyramids,  an edgeedge with one O(3)LiGd3In square pyramid, and edges with three equivalent O(2)LiGd3In trigonal bipyramids. In the third O site, O(2) is bonded to one Li(1), one Gd(2), two equivalent Gd(1), and one In(1) atom to form distorted OLiGd3In trigonal bipyramids that share corners with four equivalent O(3)LiGd3In square pyramids, corners with two equivalent O(2)LiGd3In trigonal bipyramids,  a cornercorner with one O(1)Gd3In trigonal pyramid, edges with two equivalent O(3)LiGd3In square pyramids, edges with two equivalent O(2)LiGd3In trigonal bipyramids, and edges with three equivalent O(1)Gd3In trigonal pyramids. In the fourth O site, O(3) is bonded to one Li(1), one Gd(2), two equivalent Gd(1), and one In(2) atom to form distorted OLiGd3In square pyramids that share corners with four equivalent O(2)LiGd3In trigonal bipyramids, corners with two equivalent O(1)Gd3In trigonal pyramids, edges with two equivalent O(2)LiGd3In trigonal bipyramids,  an edgeedge with one O(1)Gd3In trigonal pyramid, and faces with two equivalent O(3)LiGd3In square pyramids. is represented by the CIF file [CIF]
data_LiGd6In2O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.812
_cell_length_b   6.812
_cell_length_c   6.811
_cell_angle_alpha   93.079
_cell_angle_beta   93.083
_cell_angle_gamma   93.079
_symmetry_Int_Tables_number   1
_cell_volume   314.623
_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
  Li  Li0  1  0.214  0.214  0.214  1.0
  Gd  Gd1  1  0.067  0.588  0.257  1.0
  Gd  Gd2  1  0.257  0.067  0.588  1.0
  Gd  Gd3  1  0.441  0.740  0.936  1.0
  Gd  Gd4  1  0.588  0.257  0.067  1.0
  Gd  Gd5  1  0.740  0.936  0.441  1.0
  Gd  Gd6  1  0.936  0.441  0.740  1.0
  In  In7  1  0.981  0.981  0.981  1.0
  In  In8  1  0.498  0.498  0.498  1.0
  O  O9  1  0.098  0.686  0.928  1.0
  O  O10  1  0.075  0.935  0.313  1.0
  O  O11  1  0.183  0.394  0.514  1.0
  O  O12  1  0.313  0.075  0.935  1.0
  O  O13  1  0.394  0.514  0.183  1.0
  O  O14  1  0.463  0.808  0.603  1.0
  O  O15  1  0.514  0.183  0.394  1.0
  O  O16  1  0.603  0.463  0.808  1.0
  O  O17  1  0.686  0.928  0.098  1.0
  O  O18  1  0.808  0.603  0.463  1.0
  O  O19  1  0.928  0.098  0.686  1.0
  O  O20  1  0.935  0.313  0.075  1.0
[/CIF]
.
The compound described by LiGd6In2O12 crystallizes in the trigonal R3 space group. Li(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted LiO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids,  a faceface with one In(1)O6 octahedra,  a faceface with one In(2)O6 octahedra, and faces with three equivalent Gd(1)O6 pentagonal pyramids. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form distorted GdO6 pentagonal pyramids that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one In(1)O6 octahedra,  a cornercorner with one In(2)O6 octahedra, corners with four equivalent Gd(1)O6 pentagonal pyramids,  an edgeedge with one In(1)O6 octahedra,  an edgeedge with one In(2)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 35-38°. In the second Gd site, Gd(2) is bonded in a 6-coordinate geometry to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms. There are two inequivalent In sites. In the first In site, In(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted InO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids, edges with three equivalent Gd(1)O6 pentagonal pyramids, and  a faceface with one Li(1)O6 octahedra. In the second In site, In(2) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form InO6 octahedra that share corners with three equivalent Gd(1)O6 pentagonal pyramids, edges with three equivalent Gd(1)O6 pentagonal pyramids, and  a faceface with one Li(1)O6 octahedra. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted see-saw-like geometry to one Gd(1), two equivalent Gd(2), and one In(2) atom. In the second O site, O(1) is bonded to one Gd(1), two equivalent Gd(2), and one In(1) atom to form OGd3In trigonal pyramids that share corners with two equivalent O(3)LiGd3In square pyramids,  a cornercorner with one O(2)LiGd3In trigonal bipyramid, corners with four equivalent O(1)Gd3In trigonal pyramids,  an edgeedge with one O(3)LiGd3In square pyramid, and edges with three equivalent O(2)LiGd3In trigonal bipyramids. In the third O site, O(2) is bonded to one Li(1), one Gd(2), two equivalent Gd(1), and one In(1) atom to form distorted OLiGd3In trigonal bipyramids that share corners with four equivalent O(3)LiGd3In square pyramids, corners with two equivalent O(2)LiGd3In trigonal bipyramids,  a cornercorner with one O(1)Gd3In trigonal pyramid, edges with two equivalent O(3)LiGd3In square pyramids, edges with two equivalent O(2)LiGd3In trigonal bipyramids, and edges with three equivalent O(1)Gd3In trigonal pyramids. In the fourth O site, O(3) is bonded to one Li(1), one Gd(2), two equivalent Gd(1), and one In(2) atom to form distorted OLiGd3In square pyramids that share corners with four equivalent O(2)LiGd3In trigonal bipyramids, corners with two equivalent O(1)Gd3In trigonal pyramids, edges with two equivalent O(2)LiGd3In trigonal bipyramids,  an edgeedge with one O(1)Gd3In trigonal pyramid, and faces with two equivalent O(3)LiGd3In square pyramids. is represented by the CIF file [CIF]
data_LiGd6In2O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.812
_cell_length_b   6.812
_cell_length_c   6.811
_cell_angle_alpha   93.079
_cell_angle_beta   93.083
_cell_angle_gamma   93.079
_symmetry_Int_Tables_number   1
_cell_volume   314.623
_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
  Li  Li0  1  0.214  0.214  0.214  1.0
  Gd  Gd1  1  0.067  0.588  0.257  1.0
  Gd  Gd2  1  0.257  0.067  0.588  1.0
  Gd  Gd3  1  0.441  0.740  0.936  1.0
  Gd  Gd4  1  0.588  0.257  0.067  1.0
  Gd  Gd5  1  0.740  0.936  0.441  1.0
  Gd  Gd6  1  0.936  0.441  0.740  1.0
  In  In7  1  0.981  0.981  0.981  1.0
  In  In8  1  0.498  0.498  0.498  1.0
  O  O9  1  0.098  0.686  0.928  1.0
  O  O10  1  0.075  0.935  0.313  1.0
  O  O11  1  0.183  0.394  0.514  1.0
  O  O12  1  0.313  0.075  0.935  1.0
  O  O13  1  0.394  0.514  0.183  1.0
  O  O14  1  0.463  0.808  0.603  1.0
  O  O15  1  0.514  0.183  0.394  1.0
  O  O16  1  0.603  0.463  0.808  1.0
  O  O17  1  0.686  0.928  0.098  1.0
  O  O18  1  0.808  0.603  0.463  1.0
  O  O19  1  0.928  0.098  0.686  1.0
  O  O20  1  0.935  0.313  0.075  1.0
[/CIF]
.