The structure described by Mg14CuSn crystallizes in the hexagonal P-6m2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Cu2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10CuSn cuboctahedra. In the second Mg site, Mg(2) is bonded in a distorted linear geometry to two equivalent Mg(4), four equivalent Mg(3), and two equivalent Sn(1) atoms. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Cu(1), and one Sn(1) atom to form distorted MgMg10CuSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)Mg10CuSn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(3)Mg10CuSn cuboctahedra,  a faceface with one Cu(1)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra, and faces with six equivalent Mg(3)Mg10CuSn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with six equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg10Cu2 cuboctahedra, faces with three equivalent Cu(1)Mg12 cuboctahedra, faces with three equivalent Sn(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)Mg10CuSn cuboctahedra. Cu(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form CuMg12 cuboctahedra that share corners with six equivalent Cu(1)Mg12 cuboctahedra, edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Cu2 cuboctahedra, faces with six equivalent Mg(3)Mg10CuSn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Cu(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)Mg10CuSn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14CuSn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.266
_cell_length_b   6.266
_cell_length_c   10.327
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   351.114
_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  0.164  0.832  0.125  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.668  0.336  0.125  1.0
  Mg  Mg3  1  0.666  0.332  0.625  1.0
  Mg  Mg4  1  0.668  0.832  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.331  0.169  0.365  1.0
  Mg  Mg7  1  0.331  0.169  0.885  1.0
  Mg  Mg8  1  0.331  0.662  0.365  1.0
  Mg  Mg9  1  0.331  0.662  0.885  1.0
  Mg  Mg10  1  0.838  0.169  0.365  1.0
  Mg  Mg11  1  0.838  0.169  0.885  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Cu  Cu14  1  0.167  0.333  0.125  1.0
  Sn  Sn15  1  0.167  0.333  0.625  1.0
[/CIF]
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The structure described by Mg14CuSn crystallizes in the hexagonal P-6m2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Cu2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10CuSn cuboctahedra. In the second Mg site, Mg(2) is bonded in a distorted linear geometry to two equivalent Mg(4), four equivalent Mg(3), and two equivalent Sn(1) atoms. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Cu(1), and one Sn(1) atom to form distorted MgMg10CuSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)Mg10CuSn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(3)Mg10CuSn cuboctahedra,  a faceface with one Cu(1)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra, and faces with six equivalent Mg(3)Mg10CuSn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with six equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg10Cu2 cuboctahedra, faces with three equivalent Cu(1)Mg12 cuboctahedra, faces with three equivalent Sn(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)Mg10CuSn cuboctahedra. Cu(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form CuMg12 cuboctahedra that share corners with six equivalent Cu(1)Mg12 cuboctahedra, edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Cu2 cuboctahedra, faces with six equivalent Mg(3)Mg10CuSn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Cu2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10CuSn cuboctahedra, faces with two equivalent Cu(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)Mg10CuSn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14CuSn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.266
_cell_length_b   6.266
_cell_length_c   10.327
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   351.114
_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  0.164  0.832  0.125  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.668  0.336  0.125  1.0
  Mg  Mg3  1  0.666  0.332  0.625  1.0
  Mg  Mg4  1  0.668  0.832  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.331  0.169  0.365  1.0
  Mg  Mg7  1  0.331  0.169  0.885  1.0
  Mg  Mg8  1  0.331  0.662  0.365  1.0
  Mg  Mg9  1  0.331  0.662  0.885  1.0
  Mg  Mg10  1  0.838  0.169  0.365  1.0
  Mg  Mg11  1  0.838  0.169  0.885  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Cu  Cu14  1  0.167  0.333  0.125  1.0
  Sn  Sn15  1  0.167  0.333  0.625  1.0
[/CIF]
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