The compound described by NaMg15 crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with twelve Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(5)Mg12 cuboctahedra; faces with six equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(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)Na2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; faces with six equivalent Mg(5)Mg12 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(5), four equivalent Mg(2), and four equivalent Mg(4) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(4)NaMg11 cuboctahedra; faces with two equivalent Na(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)Na2Mg10 cuboctahedra; and faces with ten Mg(4,4)NaMg11 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 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)NaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)NaMg11 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to one Na(1); one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); and four Mg(4,4) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)NaMg11 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four Mg(4,4)NaMg11 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Na(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and four equivalent Mg(4) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)NaMg11 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(4)NaMg11 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(2); three equivalent Mg(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)NaMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_NaMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.444
_cell_length_b   6.444
_cell_length_c   10.392
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   373.726
_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
  Na  Na0  1  0.000  0.000  0.500  1.0
  Mg  Mg1  1  0.000  0.000  0.000  1.0
  Mg  Mg2  1  0.001  0.500  0.500  1.0
  Mg  Mg3  1  1.000  0.500  0.000  1.0
  Mg  Mg4  1  0.500  0.500  0.500  1.0
  Mg  Mg5  1  0.500  0.500  0.000  1.0
  Mg  Mg6  1  0.500  0.999  0.500  1.0
  Mg  Mg7  1  0.500  0.000  0.000  1.0
  Mg  Mg8  1  0.167  0.335  0.247  1.0
  Mg  Mg9  1  0.167  0.335  0.753  1.0
  Mg  Mg10  1  0.167  0.833  0.247  1.0
  Mg  Mg11  1  0.167  0.833  0.753  1.0
  Mg  Mg12  1  0.665  0.833  0.247  1.0
  Mg  Mg13  1  0.665  0.833  0.753  1.0
  Mg  Mg14  1  0.667  0.333  0.250  1.0
  Mg  Mg15  1  0.667  0.333  0.750  1.0
[/CIF]
.
The compound described by NaMg15 crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with twelve Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(5)Mg12 cuboctahedra; faces with six equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(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)Na2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; faces with six equivalent Mg(5)Mg12 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(5), four equivalent Mg(2), and four equivalent Mg(4) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(4)NaMg11 cuboctahedra; faces with two equivalent Na(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)Na2Mg10 cuboctahedra; and faces with ten Mg(4,4)NaMg11 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 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)NaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)NaMg11 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to one Na(1); one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); and four Mg(4,4) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)NaMg11 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four Mg(4,4)NaMg11 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Na(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and four equivalent Mg(4) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)NaMg11 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(4)NaMg11 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(2); three equivalent Mg(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)NaMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(4,4)NaMg11 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(4,4)NaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_NaMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.444
_cell_length_b   6.444
_cell_length_c   10.392
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   373.726
_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
  Na  Na0  1  0.000  0.000  0.500  1.0
  Mg  Mg1  1  0.000  0.000  0.000  1.0
  Mg  Mg2  1  0.001  0.500  0.500  1.0
  Mg  Mg3  1  1.000  0.500  0.000  1.0
  Mg  Mg4  1  0.500  0.500  0.500  1.0
  Mg  Mg5  1  0.500  0.500  0.000  1.0
  Mg  Mg6  1  0.500  0.999  0.500  1.0
  Mg  Mg7  1  0.500  0.000  0.000  1.0
  Mg  Mg8  1  0.167  0.335  0.247  1.0
  Mg  Mg9  1  0.167  0.335  0.753  1.0
  Mg  Mg10  1  0.167  0.833  0.247  1.0
  Mg  Mg11  1  0.167  0.833  0.753  1.0
  Mg  Mg12  1  0.665  0.833  0.247  1.0
  Mg  Mg13  1  0.665  0.833  0.753  1.0
  Mg  Mg14  1  0.667  0.333  0.250  1.0
  Mg  Mg15  1  0.667  0.333  0.750  1.0
[/CIF]
.