The crystal structure described by Mg15Li crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Li2Mg10 cuboctahedra; edges with twelve Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Li2Mg10 cuboctahedra; faces with six Mg(4,4)LiMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Li2Mg10 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(4,4)LiMg11 cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Li(1); two equivalent Mg(5); four equivalent Mg(2); and four Mg(4,4) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Li2Mg10 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(2)Li2Mg10 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Li2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Li2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)LiMg11 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Li(1); one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); and four Mg(4,4) atoms to form MgLiMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LiMg11 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four Mg(4,4)LiMg11 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Li2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Li(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and four equivalent Mg(4) atoms to form MgLiMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LiMg11 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)LiMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Li2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)LiMg11 cuboctahedra; edges with six equivalent Mg(2)Li2Mg10 cuboctahedra; edges with six Mg(4,4)LiMg11 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Li2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. is represented by the CIF card [CIF]
data_LiMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.329
_cell_length_b   6.329
_cell_length_c   10.273
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   356.407
_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  0.000  0.000  0.500  1.0
  Mg  Mg2  1  0.000  0.500  0.000  1.0
  Mg  Mg3  1  0.000  0.500  0.500  1.0
  Mg  Mg4  1  0.500  0.500  0.000  1.0
  Mg  Mg5  1  0.500  0.500  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.500  1.000  0.500  1.0
  Mg  Mg8  1  0.166  0.332  0.750  1.0
  Mg  Mg9  1  0.166  0.332  0.250  1.0
  Mg  Mg10  1  0.166  0.834  0.750  1.0
  Mg  Mg11  1  0.166  0.834  0.250  1.0
  Mg  Mg12  1  0.668  0.834  0.750  1.0
  Mg  Mg13  1  0.668  0.834  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Mg  Mg15  1  0.667  0.333  0.250  1.0
[/CIF]
.
The crystal structure described by Mg15Li crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Li2Mg10 cuboctahedra; edges with twelve Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Li2Mg10 cuboctahedra; faces with six Mg(4,4)LiMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Li2Mg10 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(4,4)LiMg11 cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Li(1); two equivalent Mg(5); four equivalent Mg(2); and four Mg(4,4) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Li2Mg10 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(2)Li2Mg10 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Li2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LiMg11 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Li2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)LiMg11 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)LiMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Li(1); one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); and four Mg(4,4) atoms to form MgLiMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LiMg11 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four Mg(4,4)LiMg11 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Li2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Li(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and four equivalent Mg(4) atoms to form MgLiMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LiMg11 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)LiMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Li2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)LiMg11 cuboctahedra; edges with six equivalent Mg(2)Li2Mg10 cuboctahedra; edges with six Mg(4,4)LiMg11 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Li2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)LiMg11 cuboctahedra. is represented by the CIF card [CIF]
data_LiMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.329
_cell_length_b   6.329
_cell_length_c   10.273
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   356.407
_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  0.000  0.000  0.500  1.0
  Mg  Mg2  1  0.000  0.500  0.000  1.0
  Mg  Mg3  1  0.000  0.500  0.500  1.0
  Mg  Mg4  1  0.500  0.500  0.000  1.0
  Mg  Mg5  1  0.500  0.500  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.500  1.000  0.500  1.0
  Mg  Mg8  1  0.166  0.332  0.750  1.0
  Mg  Mg9  1  0.166  0.332  0.250  1.0
  Mg  Mg10  1  0.166  0.834  0.750  1.0
  Mg  Mg11  1  0.166  0.834  0.250  1.0
  Mg  Mg12  1  0.668  0.834  0.750  1.0
  Mg  Mg13  1  0.668  0.834  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Mg  Mg15  1  0.667  0.333  0.250  1.0
[/CIF]
.