The compound described by Mg14TiSi crystallizes in the hexagonal P-6m2 space group. There are six 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Si2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(2)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Si2 cuboctahedra; corners with eight Mg(1,1)Mg10Ti2 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Si2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(2)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one Si(1) atom to form distorted MgMg10TiSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four Mg(1,1)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiSi cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Si2 cuboctahedra; faces with five Mg(1,1)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Ti(1), and one Si(1) atom to form distorted MgMg10TiSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiSi cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Si2 cuboctahedra; faces with five Mg(1,1)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(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)Mg10TiSi cuboctahedra; edges with six equivalent Mg(2)Mg10Si2 cuboctahedra; edges with six Mg(1,1)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Si2 cuboctahedra; faces with three Mg(1,1)Mg10Ti2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. Ti(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Si2 cuboctahedra; edges with six Mg(1,1)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(2)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Si2 cuboctahedra; faces with six Mg(3,3)Mg10TiSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14TiSi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.264
_cell_length_b   6.264
_cell_length_c   10.235
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.744
_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  0.170  0.835  0.125  1.0
  Mg  Mg1  1  0.164  0.832  0.625  1.0
  Mg  Mg2  1  0.665  0.330  0.125  1.0
  Mg  Mg3  1  0.668  0.336  0.625  1.0
  Mg  Mg4  1  0.665  0.835  0.125  1.0
  Mg  Mg5  1  0.668  0.832  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.376  1.0
  Mg  Mg7  1  0.328  0.172  0.874  1.0
  Mg  Mg8  1  0.328  0.657  0.376  1.0
  Mg  Mg9  1  0.328  0.657  0.874  1.0
  Mg  Mg10  1  0.843  0.172  0.376  1.0
  Mg  Mg11  1  0.843  0.172  0.874  1.0
  Mg  Mg12  1  0.833  0.667  0.370  1.0
  Mg  Mg13  1  0.833  0.667  0.880  1.0
  Ti  Ti14  1  0.167  0.333  0.125  1.0
  Si  Si15  1  0.167  0.333  0.625  1.0
[/CIF]
.
The compound described by Mg14TiSi crystallizes in the hexagonal P-6m2 space group. There are six 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Si2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(2)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Si2 cuboctahedra; corners with eight Mg(1,1)Mg10Ti2 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Si2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(2)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiSi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one Si(1) atom to form distorted MgMg10TiSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four Mg(1,1)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiSi cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Si2 cuboctahedra; faces with five Mg(1,1)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Ti(1), and one Si(1) atom to form distorted MgMg10TiSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Si2 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiSi cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Si2 cuboctahedra; faces with five Mg(1,1)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(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)Mg10TiSi cuboctahedra; edges with six equivalent Mg(2)Mg10Si2 cuboctahedra; edges with six Mg(1,1)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Si2 cuboctahedra; faces with three Mg(1,1)Mg10Ti2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiSi cuboctahedra. Ti(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Si2 cuboctahedra; edges with six Mg(1,1)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(2)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiSi cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Si2 cuboctahedra; faces with six Mg(3,3)Mg10TiSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14TiSi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.264
_cell_length_b   6.264
_cell_length_c   10.235
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.744
_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  0.170  0.835  0.125  1.0
  Mg  Mg1  1  0.164  0.832  0.625  1.0
  Mg  Mg2  1  0.665  0.330  0.125  1.0
  Mg  Mg3  1  0.668  0.336  0.625  1.0
  Mg  Mg4  1  0.665  0.835  0.125  1.0
  Mg  Mg5  1  0.668  0.832  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.376  1.0
  Mg  Mg7  1  0.328  0.172  0.874  1.0
  Mg  Mg8  1  0.328  0.657  0.376  1.0
  Mg  Mg9  1  0.328  0.657  0.874  1.0
  Mg  Mg10  1  0.843  0.172  0.376  1.0
  Mg  Mg11  1  0.843  0.172  0.874  1.0
  Mg  Mg12  1  0.833  0.667  0.370  1.0
  Mg  Mg13  1  0.833  0.667  0.880  1.0
  Ti  Ti14  1  0.167  0.333  0.125  1.0
  Si  Si15  1  0.167  0.333  0.625  1.0
[/CIF]
.