The crystal structure described by Mg15Ce crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Ce2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Ce(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)CeMg11 cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four equivalent Mg(4); and two equivalent Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ce(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ce2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ce(1)Mg12 cuboctahedra; faces with four Mg(2,2)Ce2Mg10 cuboctahedra; and faces with ten equivalent Mg(4)CeMg11 cuboctahedra. In the third 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 Ce(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Ce2Mg10 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)CeMg11 cuboctahedra; faces with two equivalent Mg(2)Ce2Mg10 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 equivalent Mg(4)CeMg11 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent Ce(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)CeMg11 cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Ce(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Ce2Mg10 cuboctahedra, and faces with ten equivalent Mg(4)CeMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four equivalent Mg(4); and one Ce(1) atom to form MgCeMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)CeMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ce(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ce2Mg10 cuboctahedra; edges with four equivalent Mg(4)CeMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ce(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Ce2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)CeMg11 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve equivalent Mg(4)CeMg11 cuboctahedra; edges with six Mg(2,2)Ce2Mg10 cuboctahedra; edges with six equivalent Mg(4)CeMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Ce2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Ce(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)CeMg11 cuboctahedra. Ce(1) is bonded to six Mg(2,2) and six equivalent Mg(4) atoms to form CeMg12 cuboctahedra that share corners with six equivalent Ce(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Ce2Mg10 cuboctahedra; edges with twelve equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Ce2Mg10 cuboctahedra; faces with six equivalent Mg(4)CeMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_CeMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.531
_cell_length_b   6.531
_cell_length_c   10.252
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   378.660
_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
  Ce  Ce0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.167  0.333  0.625  1.0
  Mg  Mg2  1  0.180  0.840  0.125  1.0
  Mg  Mg3  1  0.162  0.831  0.625  1.0
  Mg  Mg4  1  0.660  0.320  0.125  1.0
  Mg  Mg5  1  0.669  0.338  0.625  1.0
  Mg  Mg6  1  0.660  0.840  0.125  1.0
  Mg  Mg7  1  0.669  0.831  0.625  1.0
  Mg  Mg8  1  0.334  0.166  0.381  1.0
  Mg  Mg9  1  0.334  0.166  0.869  1.0
  Mg  Mg10  1  0.334  0.668  0.381  1.0
  Mg  Mg11  1  0.334  0.668  0.869  1.0
  Mg  Mg12  1  0.832  0.166  0.381  1.0
  Mg  Mg13  1  0.832  0.166  0.869  1.0
  Mg  Mg14  1  0.833  0.667  0.364  1.0
  Mg  Mg15  1  0.833  0.667  0.886  1.0
[/CIF]
.
The crystal structure described by Mg15Ce crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Ce2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Ce(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)CeMg11 cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four equivalent Mg(4); and two equivalent Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ce(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ce2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ce(1)Mg12 cuboctahedra; faces with four Mg(2,2)Ce2Mg10 cuboctahedra; and faces with ten equivalent Mg(4)CeMg11 cuboctahedra. In the third 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 Ce(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Ce2Mg10 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)CeMg11 cuboctahedra; faces with two equivalent Mg(2)Ce2Mg10 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 equivalent Mg(4)CeMg11 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent Ce(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)CeMg11 cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Ce(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Ce2Mg10 cuboctahedra, and faces with ten equivalent Mg(4)CeMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four equivalent Mg(4); and one Ce(1) atom to form MgCeMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)CeMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ce(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ce2Mg10 cuboctahedra; edges with four equivalent Mg(4)CeMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ce(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Ce2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)CeMg11 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve equivalent Mg(4)CeMg11 cuboctahedra; edges with six Mg(2,2)Ce2Mg10 cuboctahedra; edges with six equivalent Mg(4)CeMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Ce2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Ce(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)CeMg11 cuboctahedra. Ce(1) is bonded to six Mg(2,2) and six equivalent Mg(4) atoms to form CeMg12 cuboctahedra that share corners with six equivalent Ce(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Ce2Mg10 cuboctahedra; edges with twelve equivalent Mg(4)CeMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Ce2Mg10 cuboctahedra; faces with six equivalent Mg(4)CeMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_CeMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.531
_cell_length_b   6.531
_cell_length_c   10.252
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   378.660
_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
  Ce  Ce0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.167  0.333  0.625  1.0
  Mg  Mg2  1  0.180  0.840  0.125  1.0
  Mg  Mg3  1  0.162  0.831  0.625  1.0
  Mg  Mg4  1  0.660  0.320  0.125  1.0
  Mg  Mg5  1  0.669  0.338  0.625  1.0
  Mg  Mg6  1  0.660  0.840  0.125  1.0
  Mg  Mg7  1  0.669  0.831  0.625  1.0
  Mg  Mg8  1  0.334  0.166  0.381  1.0
  Mg  Mg9  1  0.334  0.166  0.869  1.0
  Mg  Mg10  1  0.334  0.668  0.381  1.0
  Mg  Mg11  1  0.334  0.668  0.869  1.0
  Mg  Mg12  1  0.832  0.166  0.381  1.0
  Mg  Mg13  1  0.832  0.166  0.869  1.0
  Mg  Mg14  1  0.833  0.667  0.364  1.0
  Mg  Mg15  1  0.833  0.667  0.886  1.0
[/CIF]
.