The material described by Mg14MnAl crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg10Mn2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Mn2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Mn2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg10Mn2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Mn(1); and one Al(1) atom to form MgMg10MnAl cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10MnAl cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four Mg(2,2)Mg10Mn2 cuboctahedra; edges with four Mg(3,3)Mg10MnAl cuboctahedra;  a faceface with one Mn(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; faces with five Mg(2,2)Mg10Mn2 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. In the sixth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Mn(1); and one Al(1) atom to form MgMg10MnAl cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10MnAl cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(3)Mg10MnAl cuboctahedra;  a faceface with one Mn(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; faces with five Mg(2,2)Mg10Mn2 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10MnAl cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Mg10Mn2 cuboctahedra; edges with six Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Al2 cuboctahedra; faces with three Mg(2,2)Mg10Mn2 cuboctahedra; faces with three equivalent Mn(1)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. Mn(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form MnMg12 cuboctahedra that share corners with six equivalent Mn(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Mg10Mn2 cuboctahedra; edges with twelve Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Mn2 cuboctahedra; faces with six Mg(3,3)Mg10MnAl cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Al(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Mn2 cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10MnAl cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14MnAl
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.251
_cell_length_b   6.251
_cell_length_c   10.264
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.399
_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
  Mg  Mg0  1  0.166  0.833  0.125  1.0
  Mg  Mg1  1  0.167  0.834  0.625  1.0
  Mg  Mg2  1  0.667  0.334  0.125  1.0
  Mg  Mg3  1  0.666  0.333  0.625  1.0
  Mg  Mg4  1  0.667  0.833  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.330  0.170  0.376  1.0
  Mg  Mg7  1  0.330  0.170  0.874  1.0
  Mg  Mg8  1  0.330  0.660  0.376  1.0
  Mg  Mg9  1  0.330  0.660  0.874  1.0
  Mg  Mg10  1  0.840  0.170  0.376  1.0
  Mg  Mg11  1  0.840  0.170  0.874  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Mn  Mn14  1  0.167  0.333  0.625  1.0
  Al  Al15  1  0.167  0.333  0.125  1.0
[/CIF]
.
The material described by Mg14MnAl crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg10Mn2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Mn2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Mn2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg10Mn2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10MnAl cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Mn(1); and one Al(1) atom to form MgMg10MnAl cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10MnAl cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four Mg(2,2)Mg10Mn2 cuboctahedra; edges with four Mg(3,3)Mg10MnAl cuboctahedra;  a faceface with one Mn(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; faces with five Mg(2,2)Mg10Mn2 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. In the sixth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Mn(1); and one Al(1) atom to form MgMg10MnAl cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10MnAl cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mn(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra; edges with four equivalent Mg(3)Mg10MnAl cuboctahedra;  a faceface with one Mn(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; faces with five Mg(2,2)Mg10Mn2 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10MnAl cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Mg10Mn2 cuboctahedra; edges with six Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Al2 cuboctahedra; faces with three Mg(2,2)Mg10Mn2 cuboctahedra; faces with three equivalent Mn(1)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10MnAl cuboctahedra. Mn(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form MnMg12 cuboctahedra that share corners with six equivalent Mn(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Mg10Mn2 cuboctahedra; edges with twelve Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Mn2 cuboctahedra; faces with six Mg(3,3)Mg10MnAl cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Al(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Mn2 cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10MnAl cuboctahedra; faces with two equivalent Mn(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10MnAl cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14MnAl
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.251
_cell_length_b   6.251
_cell_length_c   10.264
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.399
_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
  Mg  Mg0  1  0.166  0.833  0.125  1.0
  Mg  Mg1  1  0.167  0.834  0.625  1.0
  Mg  Mg2  1  0.667  0.334  0.125  1.0
  Mg  Mg3  1  0.666  0.333  0.625  1.0
  Mg  Mg4  1  0.667  0.833  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.330  0.170  0.376  1.0
  Mg  Mg7  1  0.330  0.170  0.874  1.0
  Mg  Mg8  1  0.330  0.660  0.376  1.0
  Mg  Mg9  1  0.330  0.660  0.874  1.0
  Mg  Mg10  1  0.840  0.170  0.376  1.0
  Mg  Mg11  1  0.840  0.170  0.874  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Mn  Mn14  1  0.167  0.333  0.625  1.0
  Al  Al15  1  0.167  0.333  0.125  1.0
[/CIF]
.