The crystal structure described by LiMg9B20 is hexagonal omega structure-derived structured and crystallizes in the triclinic P-1 space group. Li(1) is bonded to two equivalent B(1), two equivalent B(3), two equivalent B(4), two equivalent B(5), two equivalent B(6), and two equivalent B(8) atoms to form LiB12 cuboctahedra that share edges with two equivalent Mg(3)B12 cuboctahedra, edges with two equivalent Mg(4)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with six equivalent Mg(2)B12 cuboctahedra, faces with two equivalent Mg(1)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, faces with two equivalent Mg(4)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent B(1), two equivalent B(2), two equivalent B(4), two equivalent B(5), two equivalent B(8), and two equivalent B(9) atoms to form MgB12 cuboctahedra that share edges with two equivalent Mg(2)B12 cuboctahedra, edges with two equivalent Mg(3)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with six equivalent Mg(4)B12 cuboctahedra, faces with two equivalent Li(1)B12 cuboctahedra, faces with two equivalent Mg(2)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. In the second Mg site, Mg(2) is bonded to one B(1), one B(10), one B(2), one B(5), one B(6), one B(8), two equivalent B(4), two equivalent B(7), and two equivalent B(9) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(2)B12 cuboctahedra,  an edgeedge with one Mg(4)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with three equivalent Li(1)B12 cuboctahedra, edges with four equivalent Mg(3)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(2)B12 cuboctahedra,  a faceface with one Mg(3)B12 cuboctahedra, faces with two equivalent Mg(5)B12 cuboctahedra, and faces with three equivalent Mg(4)B12 cuboctahedra. In the third Mg site, Mg(3) is bonded to one B(6), one B(7), one B(8), one B(9), two equivalent B(10), two equivalent B(2), two equivalent B(3), and two equivalent B(5) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(3)B12 cuboctahedra, edges with two equivalent Mg(4)B12 cuboctahedra, edges with three equivalent Mg(5)B12 cuboctahedra, edges with four equivalent Mg(2)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(2)B12 cuboctahedra,  a faceface with one Mg(3)B12 cuboctahedra, faces with two equivalent Mg(4)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to one B(1), one B(3), one B(4), one B(5), one B(7), one B(9), two equivalent B(10), two equivalent B(6), and two equivalent B(8) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(2)B12 cuboctahedra,  an edgeedge with one Mg(4)B12 cuboctahedra, edges with two equivalent Mg(3)B12 cuboctahedra, edges with three equivalent Mg(1)B12 cuboctahedra, edges with four equivalent Mg(5)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(4)B12 cuboctahedra,  a faceface with one Mg(5)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, and faces with three equivalent Mg(2)B12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one B(10), one B(4), one B(6), one B(9), two equivalent B(1), two equivalent B(2), two equivalent B(3), and two equivalent B(7) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(5)B12 cuboctahedra, edges with two equivalent Mg(2)B12 cuboctahedra, edges with three equivalent Mg(3)B12 cuboctahedra, edges with four equivalent Mg(4)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(4)B12 cuboctahedra,  a faceface with one Mg(5)B12 cuboctahedra, faces with two equivalent Mg(2)B12 cuboctahedra, and faces with two equivalent Mg(3)B12 cuboctahedra. There are ten inequivalent B sites. In the first B site, B(1) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(5), one B(2), one B(3), and one B(8) atom. In the second B site, B(2) is bonded in a 9-coordinate geometry to one Mg(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(5), one B(1), one B(3), and one B(5) atom. In the third B site, B(3) is bonded in a 9-coordinate geometry to one Li(1), one Mg(4), two equivalent Mg(3), two equivalent Mg(5), one B(1), one B(2), and one B(5) atom. In the fourth B site, B(4) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(4), one Mg(5), two equivalent Mg(2), one B(5), one B(6), and one B(9) atom. In the fifth B site, B(5) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(3), one B(2), one B(3), and one B(4) atom. In the sixth B site, B(6) is bonded in a 9-coordinate geometry to one Li(1), one Mg(2), one Mg(3), one Mg(5), two equivalent Mg(4), one B(4), one B(7), and one B(8) atom. In the seventh B site, B(7) is bonded in a 9-coordinate geometry to one Mg(3), one Mg(4), two equivalent Mg(2), two equivalent Mg(5), one B(10), one B(6), and one B(7) atom. In the eighth B site, B(8) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(3), two equivalent Mg(4), one B(1), one B(6), and one B(9) atom. In the ninth B site, B(9) is bonded in a 9-coordinate geometry to one Mg(1), one Mg(3), one Mg(4), one Mg(5), two equivalent Mg(2), one B(10), one B(4), and one B(8) atom. In the tenth B site, B(10) is bonded in a 9-coordinate geometry to one Mg(2), one Mg(5), two equivalent Mg(3), two equivalent Mg(4), one B(10), one B(7), and one B(9) atom. is represented by the CIF file [CIF]
data_LiMg9B20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.140
_cell_length_b   7.075
_cell_length_c   7.661
_cell_angle_alpha   96.394
_cell_angle_beta   101.408
_cell_angle_gamma   115.680
_symmetry_Int_Tables_number   1
_cell_volume   286.608
_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  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.500  0.800  0.400  1.0
  Mg  Mg3  1  1.000  0.397  0.198  1.0
  Mg  Mg4  1  0.500  0.200  0.600  1.0
  Mg  Mg5  1  1.000  0.800  0.398  1.0
  Mg  Mg6  1  0.504  0.603  0.802  1.0
  Mg  Mg7  1  0.496  0.397  0.198  1.0
  Mg  Mg8  1  0.000  0.200  0.602  1.0
  Mg  Mg9  1  0.000  0.603  0.802  1.0
  B  B10  1  0.333  0.234  0.867  1.0
  B  B11  1  0.334  0.634  0.067  1.0
  B  B12  1  0.165  0.365  0.932  1.0
  B  B13  1  0.333  0.034  0.266  1.0
  B  B14  1  0.165  0.766  0.133  1.0
  B  B15  1  0.835  0.234  0.867  1.0
  B  B16  1  0.165  0.165  0.332  1.0
  B  B17  1  0.835  0.635  0.068  1.0
  B  B18  1  0.334  0.434  0.467  1.0
  B  B19  1  0.666  0.366  0.933  1.0
  B  B20  1  0.835  0.034  0.267  1.0
  B  B21  1  0.667  0.766  0.133  1.0
  B  B22  1  0.335  0.835  0.667  1.0
  B  B23  1  0.165  0.565  0.533  1.0
  B  B24  1  0.665  0.165  0.333  1.0
  B  B25  1  0.835  0.435  0.467  1.0
  B  B26  1  0.165  0.966  0.733  1.0
  B  B27  1  0.835  0.835  0.668  1.0
  B  B28  1  0.666  0.566  0.533  1.0
  B  B29  1  0.667  0.966  0.734  1.0
[/CIF]
.
The crystal structure described by LiMg9B20 is hexagonal omega structure-derived structured and crystallizes in the triclinic P-1 space group. Li(1) is bonded to two equivalent B(1), two equivalent B(3), two equivalent B(4), two equivalent B(5), two equivalent B(6), and two equivalent B(8) atoms to form LiB12 cuboctahedra that share edges with two equivalent Mg(3)B12 cuboctahedra, edges with two equivalent Mg(4)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with six equivalent Mg(2)B12 cuboctahedra, faces with two equivalent Mg(1)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, faces with two equivalent Mg(4)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent B(1), two equivalent B(2), two equivalent B(4), two equivalent B(5), two equivalent B(8), and two equivalent B(9) atoms to form MgB12 cuboctahedra that share edges with two equivalent Mg(2)B12 cuboctahedra, edges with two equivalent Mg(3)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with six equivalent Mg(4)B12 cuboctahedra, faces with two equivalent Li(1)B12 cuboctahedra, faces with two equivalent Mg(2)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. In the second Mg site, Mg(2) is bonded to one B(1), one B(10), one B(2), one B(5), one B(6), one B(8), two equivalent B(4), two equivalent B(7), and two equivalent B(9) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(2)B12 cuboctahedra,  an edgeedge with one Mg(4)B12 cuboctahedra, edges with two equivalent Mg(5)B12 cuboctahedra, edges with three equivalent Li(1)B12 cuboctahedra, edges with four equivalent Mg(3)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(2)B12 cuboctahedra,  a faceface with one Mg(3)B12 cuboctahedra, faces with two equivalent Mg(5)B12 cuboctahedra, and faces with three equivalent Mg(4)B12 cuboctahedra. In the third Mg site, Mg(3) is bonded to one B(6), one B(7), one B(8), one B(9), two equivalent B(10), two equivalent B(2), two equivalent B(3), and two equivalent B(5) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(3)B12 cuboctahedra, edges with two equivalent Mg(4)B12 cuboctahedra, edges with three equivalent Mg(5)B12 cuboctahedra, edges with four equivalent Mg(2)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(2)B12 cuboctahedra,  a faceface with one Mg(3)B12 cuboctahedra, faces with two equivalent Mg(4)B12 cuboctahedra, and faces with two equivalent Mg(5)B12 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to one B(1), one B(3), one B(4), one B(5), one B(7), one B(9), two equivalent B(10), two equivalent B(6), and two equivalent B(8) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(2)B12 cuboctahedra,  an edgeedge with one Mg(4)B12 cuboctahedra, edges with two equivalent Mg(3)B12 cuboctahedra, edges with three equivalent Mg(1)B12 cuboctahedra, edges with four equivalent Mg(5)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(4)B12 cuboctahedra,  a faceface with one Mg(5)B12 cuboctahedra, faces with two equivalent Mg(3)B12 cuboctahedra, and faces with three equivalent Mg(2)B12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one B(10), one B(4), one B(6), one B(9), two equivalent B(1), two equivalent B(2), two equivalent B(3), and two equivalent B(7) atoms to form MgB12 cuboctahedra that share  an edgeedge with one Li(1)B12 cuboctahedra,  an edgeedge with one Mg(1)B12 cuboctahedra,  an edgeedge with one Mg(5)B12 cuboctahedra, edges with two equivalent Mg(2)B12 cuboctahedra, edges with three equivalent Mg(3)B12 cuboctahedra, edges with four equivalent Mg(4)B12 cuboctahedra,  a faceface with one Li(1)B12 cuboctahedra,  a faceface with one Mg(1)B12 cuboctahedra,  a faceface with one Mg(4)B12 cuboctahedra,  a faceface with one Mg(5)B12 cuboctahedra, faces with two equivalent Mg(2)B12 cuboctahedra, and faces with two equivalent Mg(3)B12 cuboctahedra. There are ten inequivalent B sites. In the first B site, B(1) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(5), one B(2), one B(3), and one B(8) atom. In the second B site, B(2) is bonded in a 9-coordinate geometry to one Mg(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(5), one B(1), one B(3), and one B(5) atom. In the third B site, B(3) is bonded in a 9-coordinate geometry to one Li(1), one Mg(4), two equivalent Mg(3), two equivalent Mg(5), one B(1), one B(2), and one B(5) atom. In the fourth B site, B(4) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(4), one Mg(5), two equivalent Mg(2), one B(5), one B(6), and one B(9) atom. In the fifth B site, B(5) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(3), one B(2), one B(3), and one B(4) atom. In the sixth B site, B(6) is bonded in a 9-coordinate geometry to one Li(1), one Mg(2), one Mg(3), one Mg(5), two equivalent Mg(4), one B(4), one B(7), and one B(8) atom. In the seventh B site, B(7) is bonded in a 9-coordinate geometry to one Mg(3), one Mg(4), two equivalent Mg(2), two equivalent Mg(5), one B(10), one B(6), and one B(7) atom. In the eighth B site, B(8) is bonded in a 9-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(3), two equivalent Mg(4), one B(1), one B(6), and one B(9) atom. In the ninth B site, B(9) is bonded in a 9-coordinate geometry to one Mg(1), one Mg(3), one Mg(4), one Mg(5), two equivalent Mg(2), one B(10), one B(4), and one B(8) atom. In the tenth B site, B(10) is bonded in a 9-coordinate geometry to one Mg(2), one Mg(5), two equivalent Mg(3), two equivalent Mg(4), one B(10), one B(7), and one B(9) atom. is represented by the CIF file [CIF]
data_LiMg9B20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.140
_cell_length_b   7.075
_cell_length_c   7.661
_cell_angle_alpha   96.394
_cell_angle_beta   101.408
_cell_angle_gamma   115.680
_symmetry_Int_Tables_number   1
_cell_volume   286.608
_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  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.500  0.800  0.400  1.0
  Mg  Mg3  1  1.000  0.397  0.198  1.0
  Mg  Mg4  1  0.500  0.200  0.600  1.0
  Mg  Mg5  1  1.000  0.800  0.398  1.0
  Mg  Mg6  1  0.504  0.603  0.802  1.0
  Mg  Mg7  1  0.496  0.397  0.198  1.0
  Mg  Mg8  1  0.000  0.200  0.602  1.0
  Mg  Mg9  1  0.000  0.603  0.802  1.0
  B  B10  1  0.333  0.234  0.867  1.0
  B  B11  1  0.334  0.634  0.067  1.0
  B  B12  1  0.165  0.365  0.932  1.0
  B  B13  1  0.333  0.034  0.266  1.0
  B  B14  1  0.165  0.766  0.133  1.0
  B  B15  1  0.835  0.234  0.867  1.0
  B  B16  1  0.165  0.165  0.332  1.0
  B  B17  1  0.835  0.635  0.068  1.0
  B  B18  1  0.334  0.434  0.467  1.0
  B  B19  1  0.666  0.366  0.933  1.0
  B  B20  1  0.835  0.034  0.267  1.0
  B  B21  1  0.667  0.766  0.133  1.0
  B  B22  1  0.335  0.835  0.667  1.0
  B  B23  1  0.165  0.565  0.533  1.0
  B  B24  1  0.665  0.165  0.333  1.0
  B  B25  1  0.835  0.435  0.467  1.0
  B  B26  1  0.165  0.966  0.733  1.0
  B  B27  1  0.835  0.835  0.668  1.0
  B  B28  1  0.666  0.566  0.533  1.0
  B  B29  1  0.667  0.966  0.734  1.0
[/CIF]
.