The compound described by LiHo4La4O12 crystallizes in the triclinic P1 space group. Li(1) is bonded to one O(11), one O(12), one O(6), and one O(9) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Ho(1)O6 octahedra,  a cornercorner with one Ho(2)O6 octahedra,  a cornercorner with one Ho(3)O6 octahedra, and  an edgeedge with one Ho(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-74°. There are four inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to one O(1), one O(10), one O(12), one O(3), one O(5), and one O(8) atom to form HoO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra, corners with four equivalent Ho(3)O6 octahedra, and  a cornercorner with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 35-49°. In the second Ho site, Ho(2) is bonded to one O(1), one O(11), one O(12), one O(2), one O(4), and one O(9) atom to form HoO6 octahedra that share corners with two equivalent Ho(1)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, and  an edgeedge with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-49°. In the third Ho site, Ho(3) is bonded to one O(10), one O(3), one O(5), one O(6), one O(7), and one O(8) atom to form HoO6 octahedra that share corners with four equivalent Ho(1)O6 octahedra and  a cornercorner with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 35-44°. In the fourth Ho site, Ho(4) is bonded in a 6-coordinate geometry to one O(11), one O(2), one O(4), one O(6), one O(7), and one O(9) atom. There are four inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(4), one O(5), and one O(6) atom. In the second La site, La(2) is bonded in a 8-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(7), one O(8), and one O(9) atom. In the third La site, La(3) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(5), one O(6), and one O(9) atom. In the fourth La site, La(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(11), one O(2), one O(3), one O(7), one O(8), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Ho(1), one Ho(2), one La(2), and one La(4) atom to form distorted OLa2Ho2 trigonal pyramids that share  a cornercorner with one O(2)La2Ho2 tetrahedra, corners with two equivalent O(7)La2Ho2 tetrahedra,  a cornercorner with one O(3)La3Ho2 trigonal bipyramid,  an edgeedge with one O(2)La2Ho2 tetrahedra, and  an edgeedge with one O(3)La3Ho2 trigonal bipyramid. In the second O site, O(2) is bonded to one Ho(2), one Ho(4), one La(2), and one La(4) atom to form distorted OLa2Ho2 tetrahedra that share corners with three equivalent O(7)La2Ho2 tetrahedra,  a cornercorner with one O(1)La2Ho2 trigonal pyramid,  an edgeedge with one O(3)La3Ho2 trigonal bipyramid, and  an edgeedge with one O(1)La2Ho2 trigonal pyramid. In the third O site, O(3) is bonded to one Ho(1), one Ho(3), one La(1), one La(2), and one La(4) atom to form a mixture of distorted corner and edge-sharing OLa3Ho2 trigonal bipyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ho(2), one Ho(4), one La(1), one La(2), and one La(3) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ho(1), one Ho(3), one La(1), one La(2), and one La(3) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Li(1), one Ho(3), one Ho(4), one La(1), and one La(3) atom. In the seventh O site, O(7) is bonded to one Ho(3), one Ho(4), one La(2), and one La(4) atom to form distorted OLa2Ho2 tetrahedra that share corners with three equivalent O(2)La2Ho2 tetrahedra, corners with three equivalent O(3)La3Ho2 trigonal bipyramids, and corners with two equivalent O(1)La2Ho2 trigonal pyramids. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Ho(1), one Ho(3), one La(2), and one La(4) atom. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Li(1), one Ho(2), one Ho(4), one La(2), one La(3), and one La(4) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Ho(1), one Ho(3), one La(1), one La(3), and one La(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Li(1), one Ho(2), one Ho(4), one La(1), one La(3), and one La(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Li(1), one Ho(1), one Ho(2), one La(1), and one La(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiLa4Ho4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.262
_cell_length_b   8.550
_cell_length_c   5.871
_cell_angle_alpha   89.023
_cell_angle_beta   91.578
_cell_angle_gamma   91.000
_symmetry_Int_Tables_number   1
_cell_volume   314.090
_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  0.751  0.355  0.134  1.0
  La  La1  1  0.097  0.215  0.981  1.0
  La  La2  1  0.436  0.756  0.471  1.0
  La  La3  1  0.558  0.255  0.546  1.0
  La  La4  1  0.936  0.762  0.011  1.0
  Ho  Ho5  1  0.999  0.001  0.495  1.0
  Ho  Ho6  1  0.992  0.501  0.513  1.0
  Ho  Ho7  1  0.514  1.000  0.002  1.0
  Ho  Ho8  1  0.457  0.525  0.994  1.0
  O  O9  1  0.067  0.746  0.637  1.0
  O  O10  1  0.191  0.585  0.207  1.0
  O  O11  1  0.196  0.948  0.183  1.0
  O  O12  1  0.292  0.421  0.696  1.0
  O  O13  1  0.310  0.067  0.686  1.0
  O  O14  1  0.468  0.257  0.129  1.0
  O  O15  1  0.555  0.754  0.860  1.0
  O  O16  1  0.704  0.918  0.308  1.0
  O  O17  1  0.687  0.555  0.297  1.0
  O  O18  1  0.821  0.052  0.816  1.0
  O  O19  1  0.791  0.424  0.817  1.0
  O  O20  1  0.928  0.255  0.353  1.0
[/CIF]
.
The compound described by LiHo4La4O12 crystallizes in the triclinic P1 space group. Li(1) is bonded to one O(11), one O(12), one O(6), and one O(9) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Ho(1)O6 octahedra,  a cornercorner with one Ho(2)O6 octahedra,  a cornercorner with one Ho(3)O6 octahedra, and  an edgeedge with one Ho(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-74°. There are four inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to one O(1), one O(10), one O(12), one O(3), one O(5), and one O(8) atom to form HoO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra, corners with four equivalent Ho(3)O6 octahedra, and  a cornercorner with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 35-49°. In the second Ho site, Ho(2) is bonded to one O(1), one O(11), one O(12), one O(2), one O(4), and one O(9) atom to form HoO6 octahedra that share corners with two equivalent Ho(1)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, and  an edgeedge with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-49°. In the third Ho site, Ho(3) is bonded to one O(10), one O(3), one O(5), one O(6), one O(7), and one O(8) atom to form HoO6 octahedra that share corners with four equivalent Ho(1)O6 octahedra and  a cornercorner with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 35-44°. In the fourth Ho site, Ho(4) is bonded in a 6-coordinate geometry to one O(11), one O(2), one O(4), one O(6), one O(7), and one O(9) atom. There are four inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(4), one O(5), and one O(6) atom. In the second La site, La(2) is bonded in a 8-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(7), one O(8), and one O(9) atom. In the third La site, La(3) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(5), one O(6), and one O(9) atom. In the fourth La site, La(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(11), one O(2), one O(3), one O(7), one O(8), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Ho(1), one Ho(2), one La(2), and one La(4) atom to form distorted OLa2Ho2 trigonal pyramids that share  a cornercorner with one O(2)La2Ho2 tetrahedra, corners with two equivalent O(7)La2Ho2 tetrahedra,  a cornercorner with one O(3)La3Ho2 trigonal bipyramid,  an edgeedge with one O(2)La2Ho2 tetrahedra, and  an edgeedge with one O(3)La3Ho2 trigonal bipyramid. In the second O site, O(2) is bonded to one Ho(2), one Ho(4), one La(2), and one La(4) atom to form distorted OLa2Ho2 tetrahedra that share corners with three equivalent O(7)La2Ho2 tetrahedra,  a cornercorner with one O(1)La2Ho2 trigonal pyramid,  an edgeedge with one O(3)La3Ho2 trigonal bipyramid, and  an edgeedge with one O(1)La2Ho2 trigonal pyramid. In the third O site, O(3) is bonded to one Ho(1), one Ho(3), one La(1), one La(2), and one La(4) atom to form a mixture of distorted corner and edge-sharing OLa3Ho2 trigonal bipyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ho(2), one Ho(4), one La(1), one La(2), and one La(3) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ho(1), one Ho(3), one La(1), one La(2), and one La(3) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Li(1), one Ho(3), one Ho(4), one La(1), and one La(3) atom. In the seventh O site, O(7) is bonded to one Ho(3), one Ho(4), one La(2), and one La(4) atom to form distorted OLa2Ho2 tetrahedra that share corners with three equivalent O(2)La2Ho2 tetrahedra, corners with three equivalent O(3)La3Ho2 trigonal bipyramids, and corners with two equivalent O(1)La2Ho2 trigonal pyramids. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Ho(1), one Ho(3), one La(2), and one La(4) atom. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Li(1), one Ho(2), one Ho(4), one La(2), one La(3), and one La(4) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Ho(1), one Ho(3), one La(1), one La(3), and one La(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Li(1), one Ho(2), one Ho(4), one La(1), one La(3), and one La(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Li(1), one Ho(1), one Ho(2), one La(1), and one La(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiLa4Ho4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.262
_cell_length_b   8.550
_cell_length_c   5.871
_cell_angle_alpha   89.023
_cell_angle_beta   91.578
_cell_angle_gamma   91.000
_symmetry_Int_Tables_number   1
_cell_volume   314.090
_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  0.751  0.355  0.134  1.0
  La  La1  1  0.097  0.215  0.981  1.0
  La  La2  1  0.436  0.756  0.471  1.0
  La  La3  1  0.558  0.255  0.546  1.0
  La  La4  1  0.936  0.762  0.011  1.0
  Ho  Ho5  1  0.999  0.001  0.495  1.0
  Ho  Ho6  1  0.992  0.501  0.513  1.0
  Ho  Ho7  1  0.514  1.000  0.002  1.0
  Ho  Ho8  1  0.457  0.525  0.994  1.0
  O  O9  1  0.067  0.746  0.637  1.0
  O  O10  1  0.191  0.585  0.207  1.0
  O  O11  1  0.196  0.948  0.183  1.0
  O  O12  1  0.292  0.421  0.696  1.0
  O  O13  1  0.310  0.067  0.686  1.0
  O  O14  1  0.468  0.257  0.129  1.0
  O  O15  1  0.555  0.754  0.860  1.0
  O  O16  1  0.704  0.918  0.308  1.0
  O  O17  1  0.687  0.555  0.297  1.0
  O  O18  1  0.821  0.052  0.816  1.0
  O  O19  1  0.791  0.424  0.817  1.0
  O  O20  1  0.928  0.255  0.353  1.0
[/CIF]
.