The material structure described by Mg14CoSn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, corners with eight equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Co(1)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6CoSn cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Co(1), and two equivalent Sn(1) atoms to form distorted MgMg8Co2Sn2 cuboctahedra that share corners with two equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Co(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CoSn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with two equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, corners with four equivalent Co(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CoSn cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), one Co(1), and one Sn(1) atom to form distorted MgMg6CoSn cuboctahedra that share  a cornercorner with one Mg(2)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Co2Sn2 cuboctahedra,  a cornercorner with one Sn(1)Mg10Co2 cuboctahedra, corners with two equivalent Mg(1)Mg12 cuboctahedra, corners with two equivalent Co(1)Mg10Sn2 cuboctahedra, corners with four equivalent Mg(7)Mg11Sn cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Co(1)Mg10Sn2 cuboctahedra,  an edgeedge with one Sn(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(7)Mg11Sn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg10Co2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with four equivalent Mg(5)Mg6CoSn cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with six equivalent Mg(7)Mg11Sn cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Sn2 cuboctahedra. Co(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form CoMg10Sn2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form SnMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6CoSn cuboctahedra, corners with six equivalent Sn(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(5)Mg6CoSn cuboctahedra, and faces with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra. is represented by the CIF card [CIF]
data_Mg14CoSn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.274
_cell_length_b   6.280
_cell_length_c   10.126
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.036
_symmetry_Int_Tables_number   1
_cell_volume   345.406
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.169  0.835  0.625  1.0
  Mg  Mg2  1  0.672  0.337  0.125  1.0
  Mg  Mg3  1  0.666  0.330  0.625  1.0
  Mg  Mg4  1  0.672  0.835  0.125  1.0
  Mg  Mg5  1  0.666  0.835  0.625  1.0
  Mg  Mg6  1  0.328  0.173  0.362  1.0
  Mg  Mg7  1  0.328  0.173  0.888  1.0
  Mg  Mg8  1  0.328  0.655  0.362  1.0
  Mg  Mg9  1  0.328  0.655  0.888  1.0
  Mg  Mg10  1  0.845  0.172  0.365  1.0
  Mg  Mg11  1  0.845  0.172  0.885  1.0
  Mg  Mg12  1  0.833  0.666  0.379  1.0
  Mg  Mg13  1  0.833  0.666  0.871  1.0
  Co  Co14  1  0.162  0.331  0.125  1.0
  Sn  Sn15  1  0.159  0.829  0.125  1.0
[/CIF]
.
The material structure described by Mg14CoSn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, corners with eight equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Co(1)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6CoSn cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Co(1), and two equivalent Sn(1) atoms to form distorted MgMg8Co2Sn2 cuboctahedra that share corners with two equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, edges with two equivalent Co(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CoSn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with two equivalent Mg(5)Mg6CoSn cuboctahedra, corners with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, corners with four equivalent Co(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CoSn cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), one Co(1), and one Sn(1) atom to form distorted MgMg6CoSn cuboctahedra that share  a cornercorner with one Mg(2)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Co2Sn2 cuboctahedra,  a cornercorner with one Sn(1)Mg10Co2 cuboctahedra, corners with two equivalent Mg(1)Mg12 cuboctahedra, corners with two equivalent Co(1)Mg10Sn2 cuboctahedra, corners with four equivalent Mg(7)Mg11Sn cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Co(1)Mg10Sn2 cuboctahedra,  an edgeedge with one Sn(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(7)Mg11Sn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg10Co2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with four equivalent Mg(5)Mg6CoSn cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with six equivalent Mg(7)Mg11Sn cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Sn(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Sn2 cuboctahedra. Co(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form CoMg10Sn2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CoSn cuboctahedra, edges with two equivalent Sn(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form SnMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6CoSn cuboctahedra, corners with six equivalent Sn(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(7)Mg11Sn cuboctahedra, edges with four equivalent Mg(5)Mg6CoSn cuboctahedra, edges with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra, faces with two equivalent Mg(7)Mg11Sn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(5)Mg6CoSn cuboctahedra, and faces with four equivalent Mg(3)Mg8Co2Sn2 cuboctahedra. is represented by the CIF card [CIF]
data_Mg14CoSn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.274
_cell_length_b   6.280
_cell_length_c   10.126
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.036
_symmetry_Int_Tables_number   1
_cell_volume   345.406
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.169  0.835  0.625  1.0
  Mg  Mg2  1  0.672  0.337  0.125  1.0
  Mg  Mg3  1  0.666  0.330  0.625  1.0
  Mg  Mg4  1  0.672  0.835  0.125  1.0
  Mg  Mg5  1  0.666  0.835  0.625  1.0
  Mg  Mg6  1  0.328  0.173  0.362  1.0
  Mg  Mg7  1  0.328  0.173  0.888  1.0
  Mg  Mg8  1  0.328  0.655  0.362  1.0
  Mg  Mg9  1  0.328  0.655  0.888  1.0
  Mg  Mg10  1  0.845  0.172  0.365  1.0
  Mg  Mg11  1  0.845  0.172  0.885  1.0
  Mg  Mg12  1  0.833  0.666  0.379  1.0
  Mg  Mg13  1  0.833  0.666  0.871  1.0
  Co  Co14  1  0.162  0.331  0.125  1.0
  Sn  Sn15  1  0.159  0.829  0.125  1.0
[/CIF]
.